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Find x, y, z and t, if 3{bmatrix} x& y z & t{bmatrix} = {bmatr

Question

Find $x, y, z$ and $t$ , if
$3 [x z y t] = [x - 1 6 2 t] + [4 z + t x + y 3]$

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Evelyn Discussed

Find

x, y, z

and

t

, if

3 [x z y t] = [x - 1 6 2 t] + [4 z + t x + y 3]

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

3 [x z y t] = [x - 1 6 2 t] + [4 z + t x + y 3]

\Rightarrow

[3 x 3 z 3 y 3 t] = [x + 4 - 1 + z + t 6 + x + y 2 t + 3]

\Rightarrow

3 x = x + 4

\Rightarrow

3 x - x = 4

\Rightarrow

2 x = 4

∴

x = 2

Also,

\Rightarrow

3 y = 6 + x + y

\Rightarrow

3 y - y = 6 + x

\Rightarrow

2 y = 6 + x

---- ( 1 )

Substituting the value of

x

in equation ( 1 ), we get

\Rightarrow

2 y = 6 + 2

\Rightarrow

2 y = 8

\Rightarrow

y = 4

Now,

\Rightarrow

3 t == 2 t + 3

\Rightarrow

3 t - 2 t = 3

\Rightarrow

t = 3

\Rightarrow

3 z = - 1 + z + t

\Rightarrow

3 z - z = - 1 + t

\Rightarrow

2 z = - 1 + t

----- ( 2 )

Substituting the value of

t

in equation ( 2 ), we get

\Rightarrow

2 z = - 1 + 3

\Rightarrow

2 z = 2

\Rightarrow

z = 1

∴

x = 2, y = 4, z = 1

and

t = 3

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