Question

If `[(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C`, where A, B and C are matrices then find matrices B and C.

Answer 1

We have `[(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C`
Putting `lambda=0`, we get
`C=[(1,-2),(1,1)]`
Putting `lambda=1`, we get
`A+B+C=[(0, -1),(3,0)]` ...(1)
Putting `lambda=-1`, we get
`A-B+C=[(4,-3),(-3,0)]`
Subtracting (2) from (1), we get
`2B[(0, -1),(3,0)]-[(4,-3),(-3,0)]=[(-4,2),(6,0)]`
`:. B=[(-2, 1),(3,0)]`