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Learn Exercise 3.4 with Free Lessons & Tips

Find the inverse of each of the matrices, if it exists.

We know that A = IA

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Find the inverse of each of the matrices, if it exists.

We know that A = IA

Comments

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Comments

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Comments

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Comments

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Comments

Find the inverse of each of the matrices, if it exists.

We know that A = IA

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Find the inverse of each of the matrices, if it exists.

If A is the given matrix, Inverse of A = adj(A)/|A|, where |A| is the determinant of A.

We know that A = AI

where |A| = ad-bc = 1

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Comments

Find the inverse of each of the matrices, if it exists.

We know that A = AI

Comments

Find the inverse of each of the matrices, if it exists.

We know that A = AI

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Find the inverse of each of the matrices, if it exists.

We know that A = IA

As |A| = 0 , which means that the given matrix is a singular matrix.

And inverse only exists for non singular matrices.

Hence for the matrix, inverse does not exist.

 

 

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Find the inverse of each of the matrices, if it exists.

We know that A = IA

Comments

Find the inverse of each of the matrices, if it exists.

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Find the inverse of each of the matrices, if it exists.

(i)

We know that A = IA

Applying, we have:

Now, in the above equation, we can see all the zeros in the first row of the matrix on the L.H.S.

Therefore, A−1 does not exist.
(ii)

We know that A = IA

 

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Find the inverse of each of the matrices, if it exists.

We know that A = IA

Applying R2→ R2 + 3R1 and R3→ R3 − 2R1, we have:

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Find the inverse of each of the matrices, if it exists.

We know that A = IA

Applying, we have:

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Matrices A and B will be inverse of each other only if

A. AB = BA

C. AB = 0, BA = I

B. AB = BA = 0

D. AB = BA = 

Answer: D

We know that if A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is said to be the inverse of A. In this case, it is clear that A is the inverse of B.

Thus, matrices A and B will be inverses of each other only if AB = BA = I.

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