Advertisements
Advertisements
Question
State whether the following is True or False :
If A and B are conformable for the product AB, then (AB)T = ATBT.
Options
True
False
Solution
(AB)T = BTAT False.
APPEARS IN
RELATED QUESTIONS
Solve the following equations by the inversion method :
2x + 3y = - 5 and 3x + y = 3.
Find the adjoint of the following matrix.
`[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`
Find the inverse of the following matrix by the adjoint method.
`[(-1,5),(-3,2)]`
Find the inverse of the following matrix.
`[(2,0,-1),(5,1,0),(0,1,3)]`
Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.
Find the inverse of the following matrix (if they exist):
`[(3,-10),(2,-7)]`
Find the inverse of the following matrices by the adjoint method `[(3, -1),(2, -1)]`.
If A = `[(1, 2),(-3, -1)], "B" = [(-1, 0),(1, 5)]`, then AB =
Fill in the blank :
If A = `[(3, -5),(2, 5)]`, then co-factor of a12 is _______
Fill in the blank :
(AT)T = _______
State whether the following is True or False :
A(adj. A) = |A| I, where I is the unit matrix.
Check whether the following matrices are invertible or not:
`[(1, 0),(0, 1)]`
A = `[(cos alpha, - sin alpha, 0),(sin alpha, cos alpha, 0),(0, 0, 1)]`, then A−1 is
If A = `[(0, 0, -1),(0, -1, 0),(-1, 0, 0)]`, then the only correct statement about the matrix A is ______
If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1.
The value of Cofactor of element a21 in matrix A = `[(1, 2),(5, -8)]` is ______
The value of Minor of element b22 in matrix B = `[(2, -2),(4, 5)]` is ______
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
Weekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all the three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using the matrix inversion method.
Week | Number of employees | Total weekly salary (in ₹) |
||
A | B | C | ||
1st week | 4 | 2 | 3 | 4900 |
2nd week | 3 | 3 | 2 | 4500 |
3rd week | 4 | 3 | 4 | 5800 |
Which of the following matrix has no inverse
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
Solve by using matrix inversion method:
x - y + z = 2, 2x - y = 0, 2y - z = 1
The matrix M = `[(0,1,2),(1,2,3),(3,1,1)]` and its inverse is N = [nij]. What is the element n23 of matrix N?
If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = ______
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A2 - A + I = 0, then A-1 = ______.
If `A = [[-3,1],[-4,3]]` and A-1 = αA, then α = ______.
Find the cofactors of the elements of the matrix
`[(-1, 2),(-3, 4)]`
If A = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.
If A = `[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`, then A2008 is equal to ______.
If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
If the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.
If A and B are two square matrices such that A2B = BA and (AB)10 = AkB10. Then, k is ______.
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0
Find the inverse of the matrix `[(1, 1, 1),(1, 2, 3),(3, 2, 2)]` by elementary column transformation.