Given A - 2 -6- 2 0 - B- -3 2- 4 0 - C- 4 0- 0 2 - Find the matrix X such that A-2X-2B-C-

Given: A=[ 2 amp; 6; 2 amp; 0 ], B=[ 3 amp; 2; 4 amp; 0 ] and C=[ 4 amp; 0; 0 amp; 2 ] ∵ A+2X=2B+C Putting the ...

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Standard XII

Mathematics

Addition and Subtraction of a Matrix

Given A =[ 2...

Question

Given A $= [\begin{matrix} 2 & - 6 2 & 0 \end{matrix}], B = [\begin{matrix} - 3 & 2 4 & 0 \end{matrix}], C = [\begin{matrix} 4 & 0 0 & 2 \end{matrix}]$ . Find the matrix X such that $A + 2 X = 2 B + C$ .

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Solution

Given: $A = [\begin{matrix} 2 & - 6 2 & 0 \end{matrix}], B = [\begin{matrix} - 3 & 2 4 & 0 \end{matrix}]$ and $C = [\begin{matrix} 4 & 0 0 & 2 \end{matrix}]$
$∵ A + 2 X = 2 B + C$
Putting the given values, we get
$[\begin{matrix} 2 & - 6 2 & 0 \end{matrix}] + 2 X = 2 [\begin{matrix} - 3 & 2 4 & 0 \end{matrix}] + [\begin{matrix} 4 & 0 0 & 2 \end{matrix}]$
$2 X = [\begin{matrix} - 6 + 4 & 4 + 0 8 + 0 & 0 + 2 \end{matrix}] - [\begin{matrix} 2 & - 6 2 & 0 \end{matrix}]$
$X = \frac{1}{2} [\begin{matrix} - 4 & 10 6 & 2 \end{matrix}]$
$X = [\begin{matrix} - 2 & 5 3 & 1 \end{matrix}]$ .

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Given A=[2−620],B=[−3240],C=[4002]. Find the matrix X such that A+2X=2B+C.

Given: A=[2−620],B=[−3240] and C=[4002]∵A+2X=2B+CPutting the given values, we get[2−620]+2X=2[−3240]+[4002]2X=[−6+44+08+00+2]−[2−620]X=12[−41062]X=[−2531].

Given A $= [\begin{matrix} 2 & - 6 2 & 0 \end{matrix}], B = [\begin{matrix} - 3 & 2 4 & 0 \end{matrix}], C = [\begin{matrix} 4 & 0 0 & 2 \end{matrix}]$ . Find the matrix X such that $A + 2 X = 2 B + C$ .