Advertisements
Advertisements
प्रश्न
If A = `[(1 , 0),(-1 ,7)]` and I = `[(1 , 0),(0 ,1)]`, then find k so that A2 = 8A + kI.
उत्तर
We have
A = `[(1 , 0),(-1 ,7)]`
A2 = AA = `[(1 , 0),(-1 ,7)][(1 , 0),(-1 ,7)]`
= `[(1 , 0),(-8 ,49)]`
And 8A + kI = 8 `[(1 , 0),(-1 ,7)] +k [(1 , 0),(0 ,1)]`
= `[(8 , 0),(-8 , 56)] + [(k , 0),(0 , k)]`
= `[(8 + k , 0),(-8 , 56 + k)]`
Thus A2 = 8A + kI
⇒ `[(1 , 0),(-8 ,49)] = [(8 + k , 0),(-8 , 56 + k)]`
⇒ 1 = 8 + k
⇒ k = -7
Also 56 + k = 49
⇒ k = -7.
APPEARS IN
संबंधित प्रश्न
If P = `[(1, 2),(2, -1)]` and Q = `[(1, 0),(2, 1)]`, then compute:
- P2 – Q2
- (P + Q)(P – Q)
Is (P + Q)(P – Q) = P2 – Q2 true for matrix algebra?
Find the positive integers p and q such that :
`[p q][p/q]= [25]`
If M = `|(8,3),(9,7),(4,3)|` and N = `|(4,7),(5,3),(10 , 1)|` find M+N
Evaluate the following :
`|(-2 , 3),(-1 , 4)| |(6 , 4),(3 ,- 1)|`
Evaluate the following :
`|(2 , -5),(0 , -3)| |(1 , -1),(3 , 2)|`
If A = `[(9 , 1),(5 , 3)]` and B = `[(1 , 5),(7 , -11)]`, find matrix X such that 3A + 5B - 2X = 0.
If `[(x + 3, 4),(y - 4, x + y)] = [(5, 4),(3, 9)]`,find values of x and y
Choose the correct answer from the given four options :
If `[(x + 2y, 3y),(4x, 2)] = [(0, -3),(8, 2)]` then the value of x – y is
Find the values of a and below `[(a + 3, b^2 + 2),(0, -6)] = [(2a + 1, 3b),(0, b^2 - 5b)]`
If A = `[(sec60°, cos90°),(-3tan45°, sin90°)] and "B" = [(0, cos45°),(-2, 3sin90°)]` Find : A2
