Ylendsmallmatrix bigr - The value of a is

A = ([ x + y + z amp; 3; 0 amp; 12 ]) = ([ a amp; z; x+z amp; y ]). Comparing the two matrices, we get y = 12 ………………….. (1) x + y + z ...

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Standard X

Mathematics

Equality of Matrices

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Question

Consider A = $(\begin{matrix} x + y + z & 3 0 & 12 \end{matrix})$ = $(\begin{matrix} - a & z x + z & - y \end{matrix})$ . The value of a is ___

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Solution

A = $(\begin{matrix} x + y + z & 3 0 & 12 \end{matrix})$ = $(\begin{matrix} - a & z x + z & - y \end{matrix})$ .

Comparing the two matrices, we get

y = -12 ………………….. (1)

x + y + z = -a ……………………. (2)

x + z = 0 ………………….. (3)

From (2) and (3)

a = -y

= -(-12)

= 12

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Consider A = (x+y+z3012) = (−azx+z−y). The value of a is ___

A = (x+y+z3012) = (−azx+z−y). Comparing the two matrices, we get y = -12 ………………….. (1) x + y + z = -a ……………………. (2) x + z = 0 ………………….. (3) From (2) and (3) a = -y = -(-12) = 12

Consider A = $(\begin{matrix} x + y + z & 3 0 & 12 \end{matrix})$ = $(\begin{matrix} - a & z x + z & - y \end{matrix})$ . The value of a is ___