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) z = 3 ……… ...

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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)

z = 3 ……………………. (2)

x + z = 0

x = -3 ………………….. (3)

-a = x + y + z = -3 -12 +3 = -12

a = 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) z = 3 ……………………. (2) x + z = 0 x = -3 ………………….. (3) -a = x + y + z = -3 -12 +3 = -12 a = 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 _________________