Let A - - x - y y- 2x x - y - B - - 2- -1 - and C - - 3- 2 - If AB - C- then find x and y

Given: A = [ #160; #160; x + y #160; amp; y #160;; #160; #160; 2x #160; amp; x y #160; ] B= [ #160; # ...

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Byju's Answer

Standard XII

Mathematics

Transpose of a Matrix

Let A = [ x...

Question

Let $A = [\begin{matrix} x + y & y 2 x & x - y \end{matrix}], B = [\begin{matrix} 2 - 1 \end{matrix}]$ and $C = [\begin{matrix} 32 \end{matrix}] .$ If $A B = C$ , then find $x$ and $y$

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Solution

Given: $A = [\begin{matrix} x + y & y 2 x & x - y \end{matrix}]$
$B = [\begin{matrix} 2 - 1 \end{matrix}]$
$A B = [\begin{matrix} x + y & y 2 x & x - y \end{matrix}] . [\begin{matrix} 2 - 1 \end{matrix}]$
$= [\begin{matrix} 2 x + 2 y - y 4 x - x + y \end{matrix}]$
$= [\begin{matrix} 2 x + y 3 x + y \end{matrix}]$
Given $A B = C$
$\Rightarrow [\begin{matrix} 2 x + y 3 x + y \end{matrix}] = [\begin{matrix} 32 \end{matrix}]$
$\Rightarrow 2 x + y = 3$ and $3 x + y = 2$
$\Rightarrow 3 x + y - 2 x - y = 2 - 3$
$\Rightarrow x = - 1$
put $x = - 1$ in $2 x + y = 3$ we get
$\Rightarrow 2 \times - 1 + y = 3$
$\Rightarrow y = 3 + 2 = 5$
$∴ x = - 1, y = 5$

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Let A=[x+yy2xx−y],B=[2−1] and C=[32]. If AB=C, then find x and y

Given:A=[x+yy2xx−y]B=[2−1]AB=[x+yy2xx−y].[2−1]=[2x+2y−y4x−x+y]=[2x+y3x+y]Given AB=C⇒[2x+y3x+y]=[32]⇒2x+y=3 and 3x+y=2⇒3x+y−2x−y=2−3⇒x=−1put x=−1 in 2x+y=3 we get⇒2×−1+y=3⇒y=3+2=5∴x=−1,y=5

Let $A = [\begin{matrix} x + y & y 2 x & x - y \end{matrix}], B = [\begin{matrix} 2 - 1 \end{matrix}]$ and $C = [\begin{matrix} 32 \end{matrix}] .$ If $A B = C$ , then find $x$ and $y$