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Matrices — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsMatrices5 Marks
Question
Find matrix $X$ if : $X\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right)=\left(\begin{array}{lll}-7 & -8 & -9 \\ 2 & 4 & 6 \\ 11 & 10 & 9\end{array}\right)$
✓

Answer

Clearly order of $X$ is $3 \times 2$
$\text{Let}\quad X=\left(\begin{array}{ll}a & b \\c & d \\e & f\end{array}\right)$
$\begin{array}{l}\text { So } \quad\left(\begin{array}{ll}a & b \\ c & d \\ e & f\end{array}\right)\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right)=\left(\begin{array}{lll}-7 & -8 & -9 \\ 2 & 4 & 6 \\ 11 & 10 & 9\end{array}\right) \\ \left.\begin{array}{lll}a+4 b=-7 & c+4 d=2 & e+4 f=11 \\ 2 a+5 b=-8 & 2 c+5 d=4 & 2 e+5 f=10\end{array}\right\}\end{array}$
$3 a+6 b=-9,3 c+6 d=6,3 e+6 f=9$
Solving we get
$a=1, b=-2, c=2, d=0, e=-5, f=4$
Thus, $X=\left(\begin{array}{cc}1 & -2 \\ 2 & 0 \\ -5 & 4\end{array}\right)$

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