Advertisements
Advertisements
Question
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
Solution
AB = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)] [(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`
= `[(1 - 6 - 6, -1 + 4 + 3, 1 - 2+ 0),(2 - 12 - 12, -2 + 8 + 6, 2 - 4 + 0),(1 - 6 - 6, -1 + 4 + 3, 1 - 2 + 0)]`
= `[(-11, 6, -1),(-22, 12, -2),(-11, 6, -1)]`
∴ |AB| = `|(-11, 6, -1),(-22, 12, -2),(-11, 6, -1)|`
= 0 ...[∵ R1 and R3 are identical]
∴ AB is a singular matrix
BA = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)] [(1, 2, 3),(2, 4, 6),(1, 2, 3)]`
= `[(1 - 2 + 1, 2 - 4 + 2, 3 - 6 + 3),(-3 + 4 - 1, -6 + 8 - 2, -9 + 12 - 3),(-2 + 2 + 0, -4 + 4 + 0, -6 + 6 + 0)]`
= `[(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
∴ |BA| = 0
∴ BA is a singular matrix.
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|
Find the value of a, b, c, and d from the equation:
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
Find the matrix X so that X`[(1,2,3),(4,5,6)]= [(-7,-8,-9),(2,4,6)]`
If A is a square matrix such that A2 = A, then (I + A)3 – 7 A is equal to ______.
Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
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:
`[(0, 4, 7),(-4, 0, -3),(-7, 3, 0)]`
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:
`[(3, 0, 0),(0, 5, 0),(0, 0, 1/3)]`
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:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
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:
`[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
Identify the following matrix is singular or non-singular?
`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
State whether the following statement is True or False:
If A is non singular, then |A| = 0
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 = `[(1, 3, 3),(3, 1, 3),(3, 3, 1)]`, then show that A2 – 5A is a scalar matrix
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′?
If a matrix A is both symmetric and skew-symmetric, then ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
A matrix is said to be a column matrix if it has
A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are
Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| ≠ 0. Consider the following two statements:
(P) If A1I2, then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,
where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then ______.
If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.
Let A = `[(0, -2),(2, 0)]`. If M and N are two matrices given by M = `sum_(k = 1)^10 A^(2k)` and N = `sum_(k = 1)^10 A^(2k - 1)` then MN2 is ______.
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.
