Find the value of x- y and z from the following equations-iii bmatrix x-y-z lx - z y - zlendbmatrix - -beginbmatrix 9 15117endbmatrix

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Standard XII

Mathematics

Equality of Matrices

Find the valu...

Question

Find the value of x, y and z from the following equations:
$(i i i) ⎡ ⎢ ⎣ \begin{matrix} x + y + z x + z y + z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 957 \end{matrix} ⎤ ⎥ ⎦$

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Solution

Given, $⎡ ⎢ ⎣ \begin{matrix} x + y + z x + z y + z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 957 \end{matrix} ⎤ ⎥ ⎦$ . By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
x+y+z=9 ....(i)
x+z=5 ....(ii)
y+z=7 ....(iii)
Subtracting Eq. (ii) from Eq. (i), we get y =4
Subtracting Eq. (iii) from Eq. (i), we get x=2
Subtracting y=4 in Eq. (iii), we get
$4 + z = 7 \Rightarrow z = 7 - 4 = 3$
Hence, x=2, y=4, z=3

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