Advertisements
Advertisements
Question
Choose the correct alternative.
If A = `[("a", 0, 0),(0, "a", 0),(0, 0,"a")]`, then |adj.A| = _______
Options
a12
a9
a6
a–3
Solution
adj A = `[("a"^2, 0, 0),(0, "a"^2, 0),(0, 0,"a"^2)]`
∴ |adj A| = `[("a"^2, 0, 0),(0, "a"^2, 0),(0, 0,"a"^2)]`
= a6.
APPEARS IN
RELATED QUESTIONS
Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.
The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. Use this information and find the system of linear equations. Hence, find the three numbers using matrices.
x + y + z + w = 2
x − 2y + 2z + 2w = − 6
2x + y − 2z + 2w = − 5
3x − y + 3z − 3w = − 3
2x − y = 5
4x − 2y = 7
Choose the correct alternative:
If A = `[(1, 2),(2, -1)]`, then adj (A) = ______
For which values of xis the matrix
`[(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)]` non-invertible?
If A is a 3 × 3 matrix and |A| = 2, then the matrix represented by A (adj A) is equal to.
Let F(α) = `[(cosalpha, -sinalpha, 0), (sinalpha, cosalpha, 0), (0, 0, 1)]` where α ∈ R. Then [F(α)]-1 is equal to ______
Find the values of a and b if A = B, where A = `[("a" + 4, 3"b"),(8, -6)]`, B = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`
Find non-zero values of x satisfying the matrix equation:
`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`
Find A, if `[(4),(1),(3)]` A = `[(-4, 8,4),(-1, 2, 1),(-3, 6, 3)]`
If P = `[(x, 0, 0),(0, y, 0),(0, 0, z)]` and Q = `[("a", 0, 0),(0, "b", 0),(0, 0, "c")]`, prove that PQ = `[(x"a", 0, 0),(0, y"b", 0),(0, 0, z"c")]` = QP
If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (A′)′ = (AB)' = B'A'
Find the matrix A such that `[(2, -1),(1, 0),(-3, 4)] "A" = [(-1, -8, -10),(1, -2, -5),(9, 22, 15)]`
Find x, y, z if A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfies A′ = A–1.
If possible, using elementary row transformations, find the inverse of the following matrices
`[(2, 3, -3),(-1, 2, 2),(1, 1, -1)]`
In applying one or more row operations while finding A–1 by elementary row operations, we obtain all zeros in one or more, then A–1 ______.
If A = `[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)],` then ____________.