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If [1 x 1]\( \begin{bmatrix} 1&2&3 \\[0.3em] 4 & 5 &6\\[0.3em] 3 &2& 5 \end{bmatrix}\)\( \begin{bmatrix} 1 \\[0.3em] -2 \\[0.3em] 3 \end{bmatrix}\) = 0, find x.

[(1,2,3)(4,5,6)(3,2,5)] [(1,2,3)]

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Given : [1 x 1] \( \begin{bmatrix} 1&2&3 \\[0.3em] 4 & 5 &6\\[0.3em] 3 &2& 5 \end{bmatrix}\)\( \begin{bmatrix} 1 \\[0.3em] -2 \\[0.3em] 3 \end{bmatrix}\) = 0,

To find : x

Formula used :

Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj

If A is a matrix of order a x b and B is a matrix of order c x d , then matrix AB exists and is of order a x d , 

if and only if b = c

12x + 20 = 0

12x = -20

\(\text{x}=\frac{-20}{12}=\frac{-5}{3}\)

\(\text{x}=\frac{-5}{3}\)

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