If $open square brackets table row cell straight x minus straight y end cell cell 2 straight x plus straight z end cell row cell 2 straight x minus straight y end cell cell 3 straight z plus straight w end cell end table close square brackets equals open square brackets table row cell negative 1 end cell 5 row 0 13 end table close square brackets$ , find x. y. z. w

Solution

We are given that

open square brackets table row cell straight x minus straight y end cell cell 2 straight x plus straight z end cell row cell 2 straight x minus straight y end cell cell 3 straight z plus straight w end cell end table close square brackets equals open square brackets table row cell negative 1 end cell 5 row 0 13 end table close square brackets

From the definition of equality of matrices, we have,
x–y = – 1    ....(1)
2 x – y = 0    ...(2)
2.x+z = 5 ...(3)
3z + w = 13    . (4)
Subtracting (1) from (2), ,x = 1
∴ from (I), 1 – y = - 1 ;⇒ y = 2
From (3). 2 +z = 5;⇒ z = 3
From (4), 9 +' w=13;⇒ w = 4
∴ x= 1. y = 2, z= 3. w = 4

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Matrices

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