Advertisements
Advertisements
Question
Choose the correct alternative:
if A = `[(lambda, 1),(-1, -lambda)]`, then for what value of λ, A2 = 0 ?
Options
0
± 1
– 1
1
Solution
± 1
APPEARS IN
RELATED QUESTIONS
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, write The number of elements
If A = `[(sqrt(7), - 3),(- sqrt(5), 2),(sqrt(3), -5)]` then find the transpose of – A
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + (– A) = (– A) + A = 0
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of B – 5A
Find the order of the product matrix AB if
| (i) | (ii) | (iii) | (iv) | (v) | |
| Order of A | 3 × 3 | 4 × 3 | 4 × 2 | 4 × 5 | 1 × 1 |
| Order of B | 3 × 3 | 3 × 2 | 2 × 2 | 5 × 1 | 1 × 3 |
If A = `[(2, 5),(4, 3)]`, B = `[(1, -3),(2, 5)]` find AB, BA and verify AB = BA?
Given that A = `[(1, 3),(5, -1)]`, B = `[(1, -1, 2),(3, 5, 2)]`, C = `[(1, 3, 2),(-4, 1, 3)]` verify that A(B + C) = AB + AC
Show that the matrices A = `[(1, 2),(3, 1)]`, B = `[(1, -2),(-3, 1)]` satisfy commutative property AB = BA
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix AT is
Find the matrix X if 2X + `[(1, 3),(5, 7)] = [(5, 7),(9, 5)]`
If A = `[(4, 2),(-1, x)]` and such that (A – 2I)(A – 3I) = 0, find the value of x
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(4, -2),(3, -5)]`
For what value of x, the matrix A = `[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)]` is skew – symmetric
Choose the correct alternative:
Which one of the following is not true about the matrix `[(1, 0, 0),(0, 0, 0),(0, 0, 5)]`?
A matrix is an ordered:-
Let A = `((1, -1, 0),(0, 1, -1),(0, 0, 1))` and B = 7A20 – 20A7 + 2I, where I is an identity matrix of order 3 × 3. If B = [bij], then b13 is equal to ______.
Let A = `[(cosα, -sinα),(sinα, cosα)]`, α ∈ R such that A32 = `[(0, -1),(1, 0)]`. Then a value of α is ______.
