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Find the matrix A such that \(\begin{bmatrix} 2 & -1 \\[0.3em] 1 & 0 \\[0.3em] -3 & 4 \end{bmatrix}\) A = \(\begin{bmatrix} -1 & -8 & -10 \\[0.3em] 1 & -2 & -5 \\[0.3em] 9 & 22 & 15 \end{bmatrix}\)

1 Answer

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Best answer

Given,

As A is multiplied with a matrix of order 3×2 and gives a resultant matrix of order 3×3

For matrix multiplication to be possible A must have 2 rows and as resultant matrix is of 3rd order A must have 3 columns

∴ A is matrix of order 2×3

By equating the elements of 2 equal matrices we get-

a = 1 ; b = -2 and c = -5

also,

2a – d = -1 ⇒ d = 2a + 1 = 2 + 1 = 3

∴ d = 3

2b – e = -8 ⇒ e = 2b + 8 = -4 + 8 = 4

∴ e = 4

Similarly, f = 2c + 10 = 0

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