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  • If [xy 4 z+6 x+y]=[8 w 0 6] then find values of x, y, z and w.

If  \left[\begin{array}{cc} x y & 4 \\ z+6 & x+y \end{array}\right]=\left[\begin{array}{cc} 8 & w \\ 0 & 6 \end{array}\right] then find values of x, y, z and w.

Answers (1)

We are given the following matrices,

\left[\begin{array}{cc} x y & 4 \\ z+6 & x+y \end{array}\right]=\left[\begin{array}{cc} 8 & w \\ 0 & 6 \end{array}\right]

Since, both the matrices are equal, so all the elements in them are equal.

$ \therefore $ xy = 8 ; w = 4 ; z + 6 = 0\ and\ x + y = 6

Hence, we have,

\\w = 4 \\z = -6 \\$\because$ x + y = 6 \\$ \Rightarrow $ y = 6 - x \\$ \therefore $ x(6-x) = 8 \\$ \Rightarrow $ x\textsuperscript{2} - 6x + 8 = 0 \\$ \Rightarrow $ x\textsuperscript{2} - 4x - 2x + 8 = 0 \\$ \Rightarrow $ x(x - 4) - 2(x - 4) = 0 \\$ \Rightarrow $ (x - 2)(x - 4) = 0 \\$ \Rightarrow $ x = 2 or x = 4

When x = 2 ; y = 4

And when x = 4 ; y = 2

Thus, we have the values of

x = 2 or 4 ; y = 4 or 2 ; z = -6 and w = 4 

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