Question

Find the values of a. b, c and rf from the equation :

$open square brackets table row cell straight s minus straight b end cell cell 2 straight a plus straight c end cell row cell 2 straight a minus straight b end cell cell 3 straight c plus straight d end cell end table close square brackets equals open square brackets table row cell negative 1 end cell 5 row 0 13 end table close square brackets$

Solution

We are given that
$open square brackets table row cell straight s minus straight b end cell cell 2 straight a plus straight c end cell row cell 2 straight a minus straight b end cell cell 3 straight c plus straight d end cell end table close square brackets equals open square brackets table row cell negative 1 end cell 5 row 0 13 end table close square brackets$

By definition of equality of mgtijices,
a – h = - 1    ...(1)
2a – h = 0    ...(2)
2a + c‘ - 5    ,    ...(3)
3    c + d= 13    ...(4)
Subtracting (1) from (2), a = 1
∴ from (1). 1– b = – 1 ;⇒ b= 2
From (3), 2 + c = 5 ;⇒ c = 3
From (4). 9 + d = 13 ;⇒ d = 4
∴a = 1, b= 2, c = 3.d = 4

Some More Questions From Matrices Chapter

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Matrices

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