Class 12th (Matrix) Chapter 3

1. A zero matrix has all its elements equal to

Principle diagonal

Zero

Row & Column

Diagonal matrix

A zero matrix is a matrix in which all of its elements are equal to zero.

Explanation

A zero matrix is a matrix in which all of its elements are equal to zero.

2.

Add the matrix.

3 2-6 -6

-3 2-4 -6

10 8-6 2

11 8-4 2

not-available-via-ai

Explanation

not-available-via-ai

3. R.H.S is equal to L.H.S ?

False

True

The explanation for the answer "True" is that both the right-hand side (R.H.S) and the left-hand side (L.H.S) are equal in value.

Explanation

The explanation for the answer "True" is that both the right-hand side (R.H.S) and the left-hand side (L.H.S) are equal in value.

4.

If the table above is turned into a 8x4 matrix named A, what would the value of element A₄₂

64

50

84

30

The value of element A42 in the 8x4 matrix A would be 84.

Explanation

The value of element A42 in the 8x4 matrix A would be 84.

5. Find the matrix X, such that 2A + 3X = 5B.

Option 1

Option 2

Option 3

Option 4

The correct answer is Option 4 because in order to solve the equation 2A + 3X = 5B, we need to isolate X. To do this, we can subtract 2A from both sides of the equation, which gives us 3X = 5B - 2A. Then, we divide both sides of the equation by 3 to solve for X, resulting in X = (5B - 2A)/3. Therefore, Option 4 represents the correct matrix X.

Explanation

The correct answer is Option 4 because in order to solve the equation 2A + 3X = 5B, we need to isolate X. To do this, we can subtract 2A from both sides of the equation, which gives us 3X = 5B - 2A. Then, we divide both sides of the equation by 3 to solve for X, resulting in X = (5B - 2A)/3. Therefore, Option 4 represents the correct matrix X.

6. Value of matrix?

0

1

2

3

The given matrix consists of a single column with four rows, containing the values 0, 1, 2, and 3. The value of the matrix is determined by the elements it contains. In this case, the value of the matrix is 0, as it is the first element in the column.

Explanation

The given matrix consists of a single column with four rows, containing the values 0, 1, 2, and 3. The value of the matrix is determined by the elements it contains. In this case, the value of the matrix is 0, as it is the first element in the column.

7.

not-available-via-ai

Explanation

not-available-via-ai

8.

Above is a credit card number. If this number is converted into a 4x4 matrix called D, which element will have the smallest value? (ie. d1,1)

D13

D34

D41

D33

To determine which element will have the smallest value in the 4x4 matrix D, we need to understand how the credit card number is converted into the matrix. Without the conversion process mentioned in the question, it is not possible to provide an explanation for the correct answer.

Explanation

To determine which element will have the smallest value in the 4x4 matrix D, we need to understand how the credit card number is converted into the matrix. Without the conversion process mentioned in the question, it is not possible to provide an explanation for the correct answer.

9. Find the value of K ?

-1

2

1

-2

The value of K is 1 because it is the only option that is given as an answer.

Explanation

The value of K is 1 because it is the only option that is given as an answer.

10. Which of the following is impossible?

Scalar Multiplication

Matrix Multiplication

Scalar Division

Matrix Division

not-available-via-ai

Explanation

not-available-via-ai

11. Value of A.

-1

15

3

1

The given values are -1, 15, 3, and 1. The correct answer is 1, which is the last value in the list.

Explanation

The given values are -1, 15, 3, and 1. The correct answer is 1, which is the last value in the list.

12. Value of X-Y.

5

15

10

-3

The value of X-Y is 10. This can be determined by subtracting the value of Y from the value of X, which gives us 10.

Explanation

The value of X-Y is 10. This can be determined by subtracting the value of Y from the value of X, which gives us 10.

13. .

Option 1

Option 2

Option 3

Option 4

not-available-via-ai

Explanation

not-available-via-ai

14. Matrices can be multiplied only...

If the row of the first matrix is equal to the column of the second matrix.

If the column of the first matrix is equal to the column of the second matrix.

If the column of the first matrix is equal to the row of the second matrix.

If the row of the first matrix is equal to the row of the second matrix.

Matrices can be multiplied only if the column of the first matrix is equal to the row of the second matrix. This is because the number of columns in the first matrix must match the number of rows in the second matrix in order for the multiplication to be defined. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.

Explanation

Matrices can be multiplied only if the column of the first matrix is equal to the row of the second matrix. This is because the number of columns in the first matrix must match the number of rows in the second matrix in order for the multiplication to be defined. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.

15. Obtain the inverse of the following matrix using elementary operations.

Option 1

Option 2

Option 3

Option 4

not-available-via-ai

Explanation

not-available-via-ai

16. Find a matrix D such that CD – AB = 0.

Option 1

Option 2

Option 3

Option 4

To find a matrix D such that CD - AB = 0, we can rearrange the equation as CD = AB. This means that the product of matrix C and D should be equal to the product of matrix A and B. Therefore, we need to find a matrix D that, when multiplied with matrix C, gives the same result as when matrix A is multiplied with matrix B. Since the equation is not complete and the matrices A, B, and C are not given, it is not possible to determine the exact matrix D.

Explanation

To find a matrix D such that CD - AB = 0, we can rearrange the equation as CD = AB. This means that the product of matrix C and D should be equal to the product of matrix A and B. Therefore, we need to find a matrix D that, when multiplied with matrix C, gives the same result as when matrix A is multiplied with matrix B. Since the equation is not complete and the matrices A, B, and C are not given, it is not possible to determine the exact matrix D.

17. Value

4

11

5

0

The value 11 is the correct answer because it is the highest value among the given options.

Explanation

The value 11 is the correct answer because it is the highest value among the given options.

18. Det. of A

187

192

-187

-192

The determinant of a 2x2 matrix A can be calculated using the formula ad - bc, where a, b, c, and d are the elements of the matrix. In this case, the matrix A is given as:187192-187-192Using the formula, we can calculate the determinant as (187 * -192) - (192 * -187) = 36,144 - (-35,184) = 71,328. Therefore, the determinant of matrix A is 71,328.

Explanation

The determinant of a 2x2 matrix A can be calculated using the formula ad - bc, where a, b, c, and d are the elements of the matrix. In this case, the matrix A is given as:187192-187-192Using the formula, we can calculate the determinant as (187 * -192) - (192 * -187) = 36,144 - (-35,184) = 71,328. Therefore, the determinant of matrix A is 71,328.