# If [x 4 1] [(2,1,2)(1,0,2)(0,2,-4)] [x,4,-1] = 0, find x.

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If [x 4 1]$\begin{bmatrix} 2 & 1& 2 \\[0.3em] 1 & 0 & 2 \\[0.3em] 0 & 2 &-4 \end{bmatrix}$$\begin{bmatrix} \text{x} \\[0.3em] 4 \\[0.3em] -1 \end{bmatrix}$ = 0, find x.

[(2,1,2)(1,0,2)(0,2,-4)] [x,4,-1]

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Given : [x 4 1] $\begin{bmatrix} 2 & 1& 2 \\[0.3em] 1 & 0 & 2 \\[0.3em] 0 & 2 &-4 \end{bmatrix}$$\begin{bmatrix} \text{x} \\[0.3em] 4 \\[0.3em] -1 \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 d ,

if and only if b = c

2x2 + 6x + 4 = 0

x2 + 3x + 2 = 0

(x + 1)(x + 2) = 0

x + 1 = 0 or x + 2 = 0

x = -1 or x = -2

x = -1 or x = -2