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If {bmatrix}4 1 3 {bmatrix} A = {bmatrix}-1 & 8 & 4 -1 & 2 & 1

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If $⎣ ⎡ 413 ⎦ ⎤$ A = $⎣ ⎡ - 1 - 1 - 3 826413 ⎦ ⎤$ Find A

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⎣ ⎡ 413 ⎦ ⎤

A =

⎣ ⎡ - 1 - 1 - 3 826413 ⎦ ⎤

Find A

15 mins ago

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Text solutionVerified

We have XA = 3

\times

3 matrix where X is 3

\times

1. Now XA is conformable for multiplication if the number of columns in pre - factor is equal to the number of rows in the post factor . Keeping in view that the product is 3

\times

3 matrix , we must have matrix A of 1

\times

3 type i.e., A has one row and 3 columns i.e., A is row matrix
Let A = [p.q.r] say of 1

\times

3 type
Now

⎣ ⎡ 413 ⎦ ⎤

[p q r] =

⎣ ⎡ 4 p p 3 p 4 q q 3 q 4 r r 3 r ⎦ ⎤ = ⎣ ⎡ - 4 - 1 - 3 826413 ⎦ ⎤

Clearly p = -1, q = 2 and r = 1 satisfy above
Hence matrix A = (-1 2 1)

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Question Text	If $⎣ ⎡ 413 ⎦ ⎤$ A = $⎣ ⎡ - 1 - 1 - 3 826413 ⎦ ⎤$ Find A
Answer Type	Text solution:1
Upvotes	150

If ⎣⎡​413​⎦⎤​ A = ⎣⎡​−1−1−3​826​413​⎦⎤​ Find A

Text solutionVerified

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If $⎣ ⎡ 413 ⎦ ⎤$ A = $⎣ ⎡ - 1 - 1 - 3 826413 ⎦ ⎤$ Find A