Advertisements
Advertisements
Question
Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′?
Advertisements
Solution
Here, A = `[(2, 4, 0),(3, 9, 6)]`, B = `[(1, 4),(2, 8),(1, 3)]`
AB = `[(2, 4, 0),(3, 9, 6)] [(1, 4),(2, 8),(1, 3)]`
= `[(2 + 8 + 0, 8 + 32 + 0),(3 + 18 + 6, 12 + 72 + 18)]`
= `[(10, 40),(27, 102)]`
L.H.S. (AB)' = `[(10, 27),(40, 102)]`
Now B = `[(1, 4),(2, 8),(1, 3)]`
⇒ B' = `[(1, 2, 1),(4, 8, 3)]`
A = `[(2, 4, 0),(3, 9, 6)]`
⇒ A' = `[(2, 3),(4, 90),(0, 6)]`
R.H.S. B'A' = `[(1, 2, 1),(4, 8, 3)][(2, 3),(4, 9),(0, 6)]`
= `[(2 + 8 + 0, 3 + 18 + 6),(8 + 32 + 0, 12 72 + 18)]`
=`[(10, 27),(40, 102)]`
= L.H.S.
Hence, L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
`A = [a_(ij)]_(m xx n)` is a square matrix, if ______.
if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`
Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.
Given two matrices A and B
`A = [(1,-2,3),(1,4,1),(1,-3, 2)] and B = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`
find AB and use this result to solve the following system of equations:
x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(6, 0),(0, 6)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]`
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2
Select the correct option from the given alternatives:
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C
Answer the following question:
If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices
Answer the following question:
If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
Choose the correct alternative:
If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______
State whether the following statement is True or False:
If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2
If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
If two matrices A and B are of the same order, then 2A + B = B + 2A.
For the non singular matrix A, (A′)–1 = (A–1)′.
AB = AC ⇒ B = C for any three matrices of same order.
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
Show by an example that for A ≠ O, B ≠ O, AB = O
If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.
If A is a square matrix, then A – A’ is a ____________.
For any square matrix A, AAT is a ____________.
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
A diagonal matrix is said to be a scalar matrix if its diagonal elements are
Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the systems of linear equations (A2B2 – B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has ______.
If A = `[(0, -tan θ/2),(tan θ/2, 0)]` and (I2 + A) (I2 – A)–1 = `[(a, -b),(b, a)]` then 13(a2 + b2) is equal to ______.
If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.
If `A = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.
If A is a square matrix of order 3, then |2A| is equal to ______.
