Advertisements
Advertisements
प्रश्न
Determine the matrices A and B if they satisfy 2A – B + `[(6, - 6, 0),(- 4, 2, 1)]` = 0 and A – 2B = `[(3, 2, 8),(-2, 1, -7)]`
उत्तर
2A – B + `[(6, - 6, 0),(- 4, 2, 1)]` = 0
A – 2B = `[(3, 2, 8),(-2, 1, -7)]`
2A – B = `- [(6, - 6, 0),(- 4, 2, 1)]` ......(1)
A – 2B = `[(3, 2, 8),(-2, 1, -7)]` .......(2)
(1) ⇒ 2A – B + `[(6, - 6, 0),(- 4, 2, 1)]`
(2) × 2 2A – 4B = `[(3, 2, 8),(-2, 1, -7)]`
Substuting 0 + 3B = `[(6, - 6, 0),(- 4, 2, 1)] - 2[(3, 2, 8),(-2, 1, -7)]`
3B = `[(- 6, 6, 0),(4, - 2, -1)] - [(6, 4, 16),(-4, 2, -14)]`
= `[(-6 - 6, 6 - 4, 0 - 16),(4 + 4, - 2 - 2, - 1 + 14)]`
3B = `[(- 12, 2, - 16),(8, -4, 13)]`
B = `1/3[(- 12, 2, - 16),(8, -4, 13)]`
Substituting for B in equation (1)
(1) ⇒ `2"A" - 1/3 [(- 12, 2, - 6),(8, -4, 13)] = - [(6, 6, 0),(- 4, 2, 1)]`
2A = `1/3[(- 1, 2, 16),(8,-4, 13)] - [(6, -6, 0),(-4, 2, 1)]`
= `[((-12)/3, 2/3, (-16)/3),(8/3, (-4)/3, 13/3)] - [(6, -6, 0),(-4, 2, 1)]`
= `[(-4 - 6, 2/3 + 6, (- 16)/3 - 0),(8/3 + 4, (-4)/3 - 2, 13/3 - 1)]`
= `[(- 10, (2 + 8)/3, (-16)/3),((8 + 12)/3, (-4 - 6)/3, (13 - 3)/3)]`
2A = `[(- 10, 20/3, (-16)/3),(20/3, (- 10)/3, 10/3)]`
A = `1/2[(- 10, 0/3, (- 16)/3),(20/3, (- 10)/3, 10/3)]`
A = `[(-5, 10/3, (-8)/3),(10/3, (-5)/3, 5/3)]`
Reqired values are
A = `[(-5, 10/3, (-8)/3),(10/3, (-5)/3, 5/3)]`
B = `1/3[(- 12, 2, - 16),(8, -4, 13)]`
APPEARS IN
संबंधित प्रश्न
If A = `[(sqrt(7), - 3),(- sqrt(5), 2),(sqrt(3), -5)]` then find the transpose of – A
Find the values of x, y and z from the following equation
`[(12, 3),(x, 3/2)] = [(y, z),(3, 5)]`
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of 3A – 9B
Find the values of x, y, z if `[(x), (y – z), (z + 3)] + [(y), (4), (3)] = [(4), (8), (16)]`
Given that A = `[(1, 3),(5, -1)]`, B = `[(1, -1, 2),(3, 5, 2)]`, C = `[(1, 3, 2),(-4, 1, 3)]` verify that A(B + C) = AB + AC
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that A(BC) = (AB)C
If A = `[(5, 2, 9),(1, 2, 8)]`, B = `[(1, 7),(1, 2),(5, -1)]` verify that (AB)T = BT AT
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
Given A = `[("p", 0),(0, 2)]`, B = `[(0, -"q"),(1, 0)]`, C = `[(2, -2),(2, 2)]` and if BA = C2, find p and q.
Find the values of p, q, r, and s if
`[("p"^2 - 1, 0, - 31 - "q"^3),(7, "r" + 1, 9),(- 2, 8, "s" - 1)] = [(1, 0, -4),(7, 3/2, 9),(-2, 8, -pi)]`
If A = `[(4, 2),(-1, x)]` and such that (A – 2I)(A – 3I) = 0, find the value of x
If A = `[(1, 0, 0),(0, 1, 0),("a", "b", - 1)]`, show that A2 is a unit matrix
Find the matrix A which satisfies the matrix relation `"A"= [(1, 2, 3),(4, 5, 6)] = [(-7, -8, -9),(2, 4, 6)]`
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(4, -2),(3, -5)]`
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:
If A and B are two matrices such that A + B and AB are both defined, then
Choose the correct alternative:
If a ≠ b, b, c satisfy `|("a", 2"b", 2"c"),(3, "b", "c"),(4, "a", "b")|` = 0, then abc =
Choose the correct alternative:
If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC 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 ______.
