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If \( \begin{bmatrix} x & 6 \\[0.3em] -1& 2w \\[0.3em] \end{bmatrix}\) + \( \begin{bmatrix} 4 & x + y \\[0.3em] z + w& 3 \\[0.3em] \end{bmatrix}\) = 3\( \begin{bmatrix} x & y \\[0.3em] z& w \\[0.3em] \end{bmatrix}\) , find the values of x, y, z, ω.

[(x,6)(-1,2w)] + [(4, x + y)(z + w, 3)] = 3[(x,y)(z,w)]

1 Answer

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by (29.9k points)
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Best answer

Given,

First applying matrix addition then, comparing each element of the 

matrix with the corresponding element we get,

We now have, x + 4 = 3x,   .....(i)

x = 2

2w + 3 = 3w,   .......(ii)

w = 3

6 + x + y = 3y, substituting x from (i) we get,

y = 4,

And -1 + z + w = 3z, substituting w from (ii), we get,

z = 1

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