If A- -1 2- 2 -1 - and B- 3- 1 - AX-B- then X is equal to

The correct option is C 1 3 [ 5; 7 ] Given, A=[ 1 amp; 2; 2 amp; 1 ] and B=[ 3; 1 ] ∴ A ^ 1 = 1 3 [ 1 amp; 2; ...

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Standard IX

Mathematics

Transpose of a Matrix

If A=[ -1 2...

Question

If $A = [\begin{matrix} - 1 & 2 2 & - 1 \end{matrix}]$ and $B = [\begin{matrix} 31 \end{matrix}], A X = B$ , then $X$ is equal to

[\begin{matrix} 0 & 7 \end{matrix}]

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\frac{1}{3} [\begin{matrix} 57 \end{matrix}]

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\frac{1}{3} [\begin{matrix} 5 & 7 \end{matrix}]

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[\begin{matrix} 57 \end{matrix}]

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Solution

The correct option is C $\frac{1}{3} [\begin{matrix} 57 \end{matrix}]$
Given, $A = [\begin{matrix} - 1 & 2 2 & - 1 \end{matrix}]$ and $B = [\begin{matrix} 31 \end{matrix}]$
$∴ A^{- 1} = - \frac{1}{3} [\begin{matrix} - 1 & - 2 - 2 & - 1 \end{matrix}] = \frac{1}{3} [\begin{matrix} 1 & 2 2 & 1 \end{matrix}]$
and $A X = B$
$\Rightarrow X = A^{- 1} B$
$= \frac{1}{3} [\begin{matrix} 1 & 2 2 & 1 \end{matrix}] [\begin{matrix} 31 \end{matrix}]$
$= \frac{1}{3} [\begin{matrix} 3 + 2 6 + 1 \end{matrix}]$
$= \frac{1}{3} [\begin{matrix} 57 \end{matrix}]$

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If A=[−122−1] and B=[31],AX=B, then X is equal to

The correct option is C 13[57]Given, A=[−122−1] and B=[31]∴A−1=−13[−1−2−2−1]=13[1221]and AX=B⇒X=A−1B =13[1221][31] =13[3+26+1] =13[57]

If $A = [\begin{matrix} - 1 & 2 2 & - 1 \end{matrix}]$ and $B = [\begin{matrix} 31 \end{matrix}], A X = B$ , then $X$ is equal to