Advertisements
Advertisements
Question
If A = `[(1, 0, 0),(0, 1, 0),("a", "b", - 1)]`, show that A2 is a unit matrix
Solution
A = `[(1, 0, 0),(0, 1, 0),("a", "b", - 1)]`
A2 = A . A
= `[(1, 0, 0),(0, 1, 0),("a", "b", - 1)] [(1, 0, 0),(0, 1, 0),("a", "b", -1)]`
= `[(1 + 0 + 0, 0 + 0 + 0, 0 + 0 + 0),(0 + 0 + 0, 0 + 1 + 0, 0 + 0 + 0),("a" + 0 - "a", 0 + "b" - "b", 0 + 0 +1)]`
A2 = `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
Thus, A2 is a unit matrix.
APPEARS IN
RELATED QUESTIONS
Construct a 3 × 3 matrix whose elements are given by aij = `("i" + "j")^3/3`
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of 3A – 9B
Solve for x, y : `[(x^2),(y^2)] + 2[(-2x),(-y)] = [(5),(8)]`
A has ‘a’ rows and ‘a + 3’ columns. B has ‘b’ rows and ‘17 − b’ columns, and if both products AB and BA exist, find a, b?
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that (A – B)C = AC – BC
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
Construct an m × n matrix A = [aij], where aij is given by
aij = `("i" - 2"j")^2/2` with m = 2, n = 3
If A = `[(1, 0, 2), (0, 2, 1), (2, 0, 3)]` and A3 – 6A2 + 7A + kI = 0, find the value of k
Give your own examples of matrices satisfying the following conditions:
A and B such that AB ≠ BA
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0
If A is a square matrix such that A2 = A, find the value of 7A – (I + A)3
If A = `[(1, 2, 2),(2, 1, -2),(x, 2, y)]` is a matrix such that AAT = 9I, find the values of x and y
Construct the matrix A = [aij]3×3, where aij = 1 – j. State whether A is symmetric or skew–symmetric
Let A and B be two symmetric matrices. Prove that AB = BA if and only if AB is a symmetric matrix
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 = `[(cosα, -sinα),(sinα, cosα)]`, α ∈ R such that A32 = `[(0, -1),(1, 0)]`. Then a value of α is ______.
Let (p1, q1, r1) and (p2, q2, r2) are satisfying `|(1, p, p^2),(1, q, q^2),(1, r, r^2)|` = 6 (where pi, qi ri ∈ N and pi < qi < ri and i = 1, 2) and point (p1, q1, r1) lies on the plane 2x + 3y + 6z = k, and point (p2, q2, r2) lies on the plane 2x + 3y + 6z = k2 (where p1 = p2 = 1) If distance between these planes is 'd', then value of (210d) is ______.
If A = `[(1, 2),(2, 3)]` and A2 – kA – I2 = 0, then value of k is ______.
