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Question
Find the values of a, b, c and d from the following equations:`[[2a + b,a-2b],[5c-d,4c + 3d ]]`= `[[4,- 3],[11,24]]`
Solution
Since all the corresponding elements of a matrix are equal,
`⇒ 2a + b = 4 `
`⇒ b= 4 - 2a `.................................. (1)
`a - 2b = -3 `.....................................(2)
Putting the value of b in eq. (2), we get
`a-2(4-2a)= -3 `
`⇒ a-8 + 4a =-3 `
`⇒ 5a - 8 = -3 `
`⇒ 5a = -3 + 8 `
⇒ 5a = 5
`⇒ a = 1`
Putting the value of a in eq. (1), we get
`b = 4 - 2 (1)`
`⇒ b = 4-2 `
`⇒ b =2 `
`5c- d = 11`
`⇒ 5c - 11=d `...............................(3)
`4c + 3d = 24 `...............................(4)
Putting the value of d in eq. (4), we get
`4c +3 (5c-11)=24`
`⇒ 4c + 15c - 33 = 24 `
`⇒ 19c - 33 =24 `
`⇒ 19c = 24 + 33`
`⇒ 19c = 57`
`⇒ c = 57/19=3`
Putting the value of c in eq. (3), we get
`5(3)-11=d`
`⇒ 15 -11=d`
`⇒ d=4`
`∴ a=1 , b = 2, c=3 and d=4 `
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