If xbegin bmatrix 2113 1bmatrix -y beginbmatrix -1 11lend bmatrix - begin bmatrix 511end bmatrix - then find the values of x and y-

If x[ 2; 3; ]+y [ 1; 1 ]=[ 10; 5; ]⇒[ 2x+y( 1); 3x+y; ]=[ 10; 5; ] By definition of equality of matrix as the given matrices are equal, ...

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Byju's Answer

Standard XII

Mathematics

Matrix Definition and Representation

If xbegin bma...

Question

If $x [\begin{matrix} 23 \end{matrix}] + y [\begin{matrix} - 1 1 \end{matrix}] = [\begin{matrix} 105 \end{matrix}]$ , then find the values of x and y.

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Solution

If $x [\begin{matrix} 23 \end{matrix}] + y [\begin{matrix} - 1 1 \end{matrix}] = [\begin{matrix} 105 \end{matrix}] \Rightarrow [\begin{matrix} 2 x + y (- 1) 3 x + y \end{matrix}] = [\begin{matrix} 105 \end{matrix}]$
By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
2x-y=10.........(i)

and 3x+y =5 .......(ii)
Adding Eqs. (i) and (ii), we get
$5 x = 15 \Rightarrow x = 3$
Substituting x=3 in Eq. (i), we get
$2 \times 3 - y = 10 \Rightarrow y = 6 - 10 = - 4$

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If x[23]+y[−11]=[105], then find the values of x and y.

If $x [\begin{matrix} 23 \end{matrix}] + y [\begin{matrix} - 1 1 \end{matrix}] = [\begin{matrix} 105 \end{matrix}]$ , then find the values of x and y.