If A is a non–singular matrix and the eigen values of A are 2 , 3 , -3 then the eigen values of A-1area)2 , 3 , - 3b)1/2, 1/3, -1/3c)2|A|, 3|A|, -3|A|d)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

If A is a non&#8211;singular matrix and the eigen values of A are 2 , 3 , -3 then the eigen values of A-1area)2 , 3 , - 3b)1/2, 1/3, -1/3c)2|A|, 3|A|, -3|A|d)None of theseCorrect answer is option 'B'. Can you explain this answer?

Answer

-negative integer, then the absolute value of A is simply the positive version of A, since a non-negative integer is already positive or zero. Therefore, the absolute value of A is simply A.

Answer

-numeric value, it cannot be converted to a numeric value. Therefore, any mathematical operation involving A and a numeric value will result in an error.

Answer

-negative real number, then A raised to any power will also be a non-negative real number.

For example, if A = -2, then A^2 = 4, A^3 = -8, A^4 = 16, and so on. However, if A is a positive real number, then A raised to any power can be either positive or negative.

For example, if A = 2, then A^2 = 4, A^3 = 8, A^4 = 16, and so on. But if A = -2, then A^2 = 4, A^3 = -8, A^4 = 16, and so on.

Therefore, it is important to consider the sign of A before raising it to a power.

Answer

We know that, if a, b and c are eigen values for A

the eigen values for A-1 will be =(1/a), (1/b) and (1/c)

therefore, (1/2), (1/3) and (-1/3)

Answer

-negative integer, then the absolute value of A is equal to the negative of A.

For example, if A = -5, then |A| = 5 and -A = 5.

However, if A is a positive integer or zero, then the absolute value of A is equal to A itself.

For example, if A = 3, then |A| = 3 and -A = -3, which is not the same as |A|.

Therefore, the rule for finding the absolute value of a number depends on whether the number is positive or negative.

Answer

B

Answer

Non Singular means | A | is not equal to Zero Eigen values  In form of | A-λ I | = 0 Then  A-1 Is 1/2,1/3, - 1/3

Answer

For non singular matrix the Eigen values of A inverse are reciprocal of the eigen values of A

Answer

1/a,1/b,1/c are eigen values of A^-1

Answer

Explain anyone with any example

Answer

C

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