If - x-y 1 z- 2x-y 0 w - - -1 1 4- 0 0 5 - find x- y- z- w-

From the properties of matrices, [ a amp; b; c amp; d ]= #160;[ A amp; B; C amp; D ]⇒ A=a, B= b, C= c+ D= d. So, x y=1 amp; ...

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Byju's Answer

Standard XII

Mathematics

Matrix Definition and Representation

If [ x-y 1...

Question

If $[\begin{matrix} x - y & 1 & z 2 x - y & 0 & w \end{matrix}] = [\begin{matrix} - 1 & 1 & 4 0 & 0 & 5 \end{matrix}]$ find $x, y, z, w .$

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Solution

From the properties of matrices,
$[\begin{matrix} a & b c & d \end{matrix}] = [\begin{matrix} A & B C & D \end{matrix}] \Rightarrow A = a, B = b, C = c + D = d .$
So, $x - y = 1$ & $2 x - y = 0.$
$1 = 1$ & $0 = 0$ .
$Z = 4$ & $W = 5$
Now, we get two linear equation :
$x - y = - 1 \to (1)$
$2 x - y = 0 \to (2)$
From $(1)$ & $(2)$ . We get $x = 1$ & $y = 2$ .
So the value of $x, y, z$ is $1, 2, 4, 5$ respectively.

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If [x−y1z2x−y0w]=[−114005] find x,y,z,w.

From the properties of matrices,[abcd]=[ABCD]⇒A=a,B=b,C=c+D=d.So, x−y=1 & 2x−y=0.1=1 & 0=0.Z=4 & W=5Now, we get two linear equation :x−y=−1→(1)2x−y=0→(2)From (1) & (2). We get x=1 & y=2.So the value of x,y,z is 1,2,4,5 respectively.

If $[\begin{matrix} x - y & 1 & z 2 x - y & 0 & w \end{matrix}] = [\begin{matrix} - 1 & 1 & 4 0 & 0 & 5 \end{matrix}]$ find $x, y, z, w .$