02.11.2021

What is the value of the element in row 1, column 1 of matrix X?
4
8y
0

. 5

Faq

Mathematics
Step-by-step answer
P Answered by PhD

Option A is correct.

Step-by-step explanation:

We given with \begin{bmatrix}4&y\\0&1\end{bmatrix}X=\begin{bmatrix}y\\4\end{bmatrix}

We have to find Element in row 1 and column 1 of Matrix C.

Matrix C is Matrix X.

So, we have

X=\begin{bmatrix}4&y\\0&1\end{bmatrix}^{-1}\begin{bmatrix}y\\4\end{bmatrix}

So first we find inverse of first matrix,

Inverse of matrix A is given by \frac{1}{\left|A\right|}Adj\,A

let, A=\begin{bmatrix}4&y\\0&1\end{bmatrix}

then,

Adj\,A=\begin{bmatrix}1&-y\\0&4\end{bmatrix}

|A| = 4 × 1 - 0 × y = 4

So, X=\frac{1}{\left|A\right|}Adj\,A\times\begin{bmatrix}y\\4\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}1&-y\\0&4\end{bmatrix}\begin{bmatrix}y\\4\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}1\times y+(-y)\times4\\0\times y+4\times4\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}y-4y\\16\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}-3y\\16\end{bmatrix}

=\begin{bmatrix}\frac{-3y}{4}\\\frac{16}{4}\end{bmatrix}

=\begin{bmatrix}\frac{-3y}{4}\\4\end{bmatrix}

Element at row 1 and column 1 of matrix is \frac{-3y}{4}

Therefore, Option A is correct.

Mathematics
Step-by-step answer
P Answered by PhD

Option A is correct.

Step-by-step explanation:

We given with \begin{bmatrix}4&y\\0&1\end{bmatrix}X=\begin{bmatrix}y\\4\end{bmatrix}

We have to find Element in row 1 and column 1 of Matrix C.

Matrix C is Matrix X.

So, we have

X=\begin{bmatrix}4&y\\0&1\end{bmatrix}^{-1}\begin{bmatrix}y\\4\end{bmatrix}

So first we find inverse of first matrix,

Inverse of matrix A is given by \frac{1}{\left|A\right|}Adj\,A

let, A=\begin{bmatrix}4&y\\0&1\end{bmatrix}

then,

Adj\,A=\begin{bmatrix}1&-y\\0&4\end{bmatrix}

|A| = 4 × 1 - 0 × y = 4

So, X=\frac{1}{\left|A\right|}Adj\,A\times\begin{bmatrix}y\\4\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}1&-y\\0&4\end{bmatrix}\begin{bmatrix}y\\4\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}1\times y+(-y)\times4\\0\times y+4\times4\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}y-4y\\16\end{bmatrix}

=\frac{1}{4}\begin{bmatrix}-3y\\16\end{bmatrix}

=\begin{bmatrix}\frac{-3y}{4}\\\frac{16}{4}\end{bmatrix}

=\begin{bmatrix}\frac{-3y}{4}\\4\end{bmatrix}

Element at row 1 and column 1 of matrix is \frac{-3y}{4}

Therefore, Option A is correct.

Computers and Technology
Step-by-step answer
P Answered by PhD

The Matlab commands for the given index operations and corresponding outputs are given below.

Explanation:

clc   % is used to clear the command window of the Matlab

clear all   % is used to clear the variables stored in Matlab workspace

% We are given a 4x4 matrix

Matlab command:

M = [16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]

output:

M =

   16     2     3    13

    5    11    10     8

    9     7     6    12

    4    14    15     1

(a) The value in the first row and second column (ie. 2)

Matlab command:

a = M(1,2)

% where a = Matrix(row_1,column_2)

output:

a =

    2

(b) The value in the third row and third column (ie. 6)

Matlab command:

b = M(3,3)

% where b = Matrix(row_3,column_3)

output:

b =

     6  

(c) All the elements in the first row

Matlab command:

c = M(1,:)

% where c = Matrix(row_1,:)

output:

c =

   16     2     3    13

(d) All the elements in the second column

Matlab command:

d = M(:,2)

% where d = Matrix(:,column_2)

output:

d =

    2

   11

    7

   14

(e) All the elements in the first 2 rows (row 1 & 2)

Matlab command:

e = M([1,2],:)

% where e = Matrix([row_1,row_2],:)

output:

e =

   16     2     3    13

    5    11    10     8  

(f) All the elements in the last 2 columns (columns 3 & 4)

Matlab command:

f = M(:,[3,4])

% where f= Matrix(:,[column_3,column_4])

output:

f =  

    3    13

   10     8

    6    12

   15     1

(g) The elements 3 13 10 8

Matlab command:

g = [M(1,3) M(1,4); M(2,3) M(2,4)]

% where g = Matrix(row_1,column_3) M(row_1,column_4); M(row_2,column_3), M(row_2,column_4)

output:

g =

    3    13

   10     8

Computers and Technology
Step-by-step answer
P Answered by PhD

The Matlab commands for the given index operations and corresponding outputs are given below.

Explanation:

clc   % is used to clear the command window of the Matlab

clear all   % is used to clear the variables stored in Matlab workspace

% We are given a 4x4 matrix

Matlab command:

M = [16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]

output:

M =

   16     2     3    13

    5    11    10     8

    9     7     6    12

    4    14    15     1

(a) The value in the first row and second column (ie. 2)

Matlab command:

a = M(1,2)

% where a = Matrix(row_1,column_2)

output:

a =

    2

(b) The value in the third row and third column (ie. 6)

Matlab command:

b = M(3,3)

% where b = Matrix(row_3,column_3)

output:

b =

     6  

(c) All the elements in the first row

Matlab command:

c = M(1,:)

% where c = Matrix(row_1,:)

output:

c =

   16     2     3    13

(d) All the elements in the second column

Matlab command:

d = M(:,2)

% where d = Matrix(:,column_2)

output:

d =

    2

   11

    7

   14

(e) All the elements in the first 2 rows (row 1 & 2)

Matlab command:

e = M([1,2],:)

% where e = Matrix([row_1,row_2],:)

output:

e =

   16     2     3    13

    5    11    10     8  

(f) All the elements in the last 2 columns (columns 3 & 4)

Matlab command:

f = M(:,[3,4])

% where f= Matrix(:,[column_3,column_4])

output:

f =  

    3    13

   10     8

    6    12

   15     1

(g) The elements 3 13 10 8

Matlab command:

g = [M(1,3) M(1,4); M(2,3) M(2,4)]

% where g = Matrix(row_1,column_3) M(row_1,column_4); M(row_2,column_3), M(row_2,column_4)

output:

g =

    3    13

   10     8

Computers and Technology
Step-by-step answer
P Answered by Specialist

See Explanation

Explanation:

The line by line explanation of the modified program is as follows:

(1)

min is declared and initialized to the highest possible integer and max is declared and initialized to the least possible integer

int min,max;

min = Integer.MAX_VALUE; max = Integer.MIN_VALUE;

This iterates through each row. Because each row has a different number of elements, the row length of each is calculated using data[row].length

for ( int col=0; col< data[row].length; col++){

The following if statements get the minimum and the maximum elements of the array

   if(data[row][col] < min){         min = data[row][col];    }

   if(data[row][col] > max){         max = data[row][col];     }

(2):

The loop remains the same, however, the print statement is adjusted upward to make comparison between each row and the highest of each row is printed after the comparison

for ( int row=0; row < data.length; row++){

for ( int col=0; col< data[row].length; col++){

   if(data[row][col] > max){         max = data[row][col];     }

}

System.out.println( "max = " + max);

max = Integer.MIN_VALUE; }

See attachment for complete program that answers (1) and (2)

Computers and Technology
Step-by-step answer
P Answered by Specialist

See Explanation

Explanation:

The line by line explanation of the modified program is as follows:

(1)

min is declared and initialized to the highest possible integer and max is declared and initialized to the least possible integer

int min,max;

min = Integer.MAX_VALUE; max = Integer.MIN_VALUE;

This iterates through each row. Because each row has a different number of elements, the row length of each is calculated using data[row].length

for ( int col=0; col< data[row].length; col++){

The following if statements get the minimum and the maximum elements of the array

   if(data[row][col] < min){         min = data[row][col];    }

   if(data[row][col] > max){         max = data[row][col];     }

(2):

The loop remains the same, however, the print statement is adjusted upward to make comparison between each row and the highest of each row is printed after the comparison

for ( int row=0; row < data.length; row++){

for ( int col=0; col< data[row].length; col++){

   if(data[row][col] > max){         max = data[row][col];     }

}

System.out.println( "max = " + max);

max = Integer.MIN_VALUE; }

See attachment for complete program that answers (1) and (2)

Computers and Technology
Step-by-step answer
P Answered by PhD

Following are the code to this question:

public class ArrayMath//defining a class ArrayMath

{

public static void main(String[] args) //defining main method

{

int x[][]=new int[10][10]; //defining a 2D array  

arrays(x);//calling a method arrays by passing an array

}

private static void arrays(int[][] x)//defining a method arrays

{

int odd_column_sum=0,sum_of_Elements=0,i,j,even=1;//defining integer variable  

for(i=0;i<x.length;i++)//defining loop for columns  

{

for(j=0;j<x[0].length;j++)//defining loop for rows

{

x[i][j]=i*j;//multiply the i and j value atore in array

}

}

System.out.println("::The 2D array :: ");//print message

for(i=0;i<x.length;i++)//defining loop for columns

{

System.out.print("\t");//use print method for line space and line break  

for(j=0;j<x[0].length;j++)//defining loop for rows

{

System.out.printf("%d\t",x[i][j]); //print array values

}

System.out.println( );//print for line break

}

for(i=0;i<x.length;i++) //defining loop for Columns

{

for(j=0;j<x[0].length;j++) //defining loop for rows

{

if(even%2!=0)//defining if block for check odd number condition

{

odd_column_sum+=x[j][i];//add odd number of array

}

sum_of_Elements+=x[i][j];//add even number of array

}

even++;//increment even variable value by 1

}

System.out.println("The sum of Odd Columns:"+odd_column_sum);//print odd_column_sum value

System.out.println("The array elements :"+sum_of_Elements);//print sum_of_Elements value

}

}

Output:

please find attached file.

Explanation:

In the above-given code, a class "ArrayMath" is defined, inside the class the main method is declared, which define a 2D array "x", this stores 10 columns and 10 rows and at the last, we call the arrays method by passing an array as a variable.

In the arrays method, integer variable, "odd_column_sum, sum_of_Elements, i, j, and even" is defined, in which variable "i and j" is used in the loop for calculating value, even is used to check odd column and then store its value in the "odd_column_sum" variable, and add whole element value is added into the "sum_of_Elements" variable.


- Create a Java program in both Windows and Ubuntu using any of their Editors *** DO NOT USE IDE'S S
StudenGPT
Step-by-step answer
P Answered by Studen AI
1. Atomic radius refers to the size of an atom, specifically the distance from the nucleus to the outermost electron shell. When we observe the trends in atomic radius across a period or down a group of elements in the periodic table, the following patterns are observed:

- Across a period (row): The atomic radius generally decreases from left to right within a period. This happens because as we move from left to right, the number of protons in the nucleus increases, which increases the positive charge attracting the electrons. Due to this stronger pull from the nucleus, the electron cloud contracts, resulting in a smaller atomic radius.

- Down a group (column): The atomic radius generally increases from top to bottom within a group. This occurs because as we move down a group, the number of electron shells or energy levels increases. The outermost electrons are located in higher energy levels that are farther away from the nucleus. The increase in electron-electron repulsion also contributes to the expansion of the atomic radius.

2. Anions are larger than neutral atoms of the same element because anions have gained extra electrons. When an atom gains an electron (forming an anion), the additional electron(s) are added to the outermost electron shell. These additional electrons experience repulsion from the existing electrons in the atom, resulting in an expansion of the electron cloud and a larger atomic radius. Therefore, anions are larger than neutral atoms.

3. The ionization energy refers to the energy required to remove an electron from an atom or ion. There are two trends in ionization energy as we move across rows and down columns of the periodic table:

- Across a period (row): Ionization energy generally increases from left to right within a period. This happens because as we move from left to right, the atomic radius decreases, and the outermost electrons are held more tightly by the stronger attraction from the increasing number of protons in the nucleus. Therefore, more energy is required to remove an electron, resulting in higher ionization energy.

- Down a group (column): Ionization energy generally decreases from top to bottom within a group. This occurs because as we move down a group, the atomic radius increases, and the outermost electrons are located farther away from the nucleus. The increased distance reduces the attractive force between the nucleus and the outermost electrons, making it easier to remove an electron with less energy, resulting in lower ionization energy.

4. True. Ionization energy values are always positive because work has to be done in order to remove an electron from an atom or ion. The positive ionization energy represents the energy required to overcome the attractive forces between the negatively charged electron and the positively charged nucleus. However, it is important to note that ionization energy can vary in magnitude depending on the specific element and electron being removed.

5. Electron affinity refers to the energy change when an electron is added to a neutral atom to form a negative ion (anion). The trends in electron affinity are as follows:

- Across a period (row): Electron affinity generally increases from left to right within a period. This is because as we move from left to right, the atomic radius decreases, meaning that the added electron is closer to the nucleus. The higher positive charge in the nucleus attracts the additional electron more strongly, resulting in a higher electron affinity.

- Down a group (column): Electron affinity generally decreases from top to bottom within a group. This occurs because as we move down a group, the atomic radius increases, and the outermost electrons are located farther away from the nucleus. The increased distance reduces the attractive force between the nucleus and the added electron, resulting in a lower electron affinity.

6. Energy input is required to add an electron to zinc because adding an electron to zinc results in the formation of a negatively charged ion (anion). Zinc is a transition metal, and its electron configuration is [Ar] 3d10 4s2. The electron being added would occupy a 3d orbital, which is already partially filled. Due to the electron-electron repulsion within the partially filled 3d orbital, it requires additional energy to overcome this repulsion and add an electron to the atom. Therefore, energy input is required to add an electron to zinc.
Mathematics
Step-by-step answer
P Answered by Specialist

1) a. False, adding a multiple of one column to another does not change the value of the determinant.

2) d. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.

Step-by-step explanation:

1) If the multiple of one column of a matrix A is added to another to form matrix B then we get: |A| = |B|. Here, the value of the determinant does not change. The correct option is A

a. False, adding a multiple of one column to another does not change the value of the determinant.

2) Two matrices can be column-equivalent when one matrix is changed to the other using a sequence of elementary column operations. Correc option is d.

d. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.

Mathematics
Step-by-step answer
P Answered by Specialist

1) a. False, adding a multiple of one column to another does not change the value of the determinant.

2) d. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.

Step-by-step explanation:

1) If the multiple of one column of a matrix A is added to another to form matrix B then we get: |A| = |B|. Here, the value of the determinant does not change. The correct option is A

a. False, adding a multiple of one column to another does not change the value of the determinant.

2) Two matrices can be column-equivalent when one matrix is changed to the other using a sequence of elementary column operations. Correc option is d.

d. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.

Try asking the Studen AI a question.

It will provide an instant answer!

FREE