Advertisements
Advertisements
Question
Find the matrix A such that `[(2, -1),(1, 0),(-3, 4)]"A"^"T" = [(-1, -8, -10),(1, 2, -5),(9, 22, 15)]`
Solution
`[(2, -1),(1, 0),(-3, 4)]"A"^"T" = [(-1, -8, -10),(1, 2, -5),(9, 22, 15)]`
Let AT = `[("a", "b","c"),("d", "e", "f")]` then
`[(2, -1),(1, 0),(-3, 4)] [("a", "b","c"),("d", "e", "f")] = [(-1, -8, -10),(1, 2, -5),(9, 22, 15)]`
`[(2"a" - "d", 2"b" - "e", 2"c" - "f"),("a" + 0, "b" + 0, "c" + 0),(-3"a" + "d", -3"b" + 4"e", -3"c" + 4"f")] = [(-1, -8, -10),(1, 2, -5),(9, 22, 15)]`
Equating like entries
2a – d = –1, 2b – e = – 8, 2c – f = – 10
a = 1, b = 2, c = -5
2a – d = – 1
⇒ 2 × 1 – d = – 1
⇒ 2 + 1 = d
⇒ d = 3
2b – e = – 8
⇒ 2 × 2 – e
= – 8
⇒ 4 + 8 = e
⇒ e = 12
2c – f = – 10
⇒ 2 × – 5 – f = – 10
⇒ – 10 – f = – 10
⇒ f = 0
∴ AT = `[(1, 2, -5),(3, 12, 0)]`
A = `[(1, 3),(2, 12),(-5, 0)]`
APPEARS IN
RELATED QUESTIONS
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, Write the elements a22, a23, a24, a34, a43, a44
If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?
Find the values of x, y and z from the following equation
`[(x + y + z),(x + z),(y + z)] = [(9),(5),(7)]`
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + B = B + A
Find X and Y if X + Y = `[(7, 0),(3, 5)]` and X – Y = `[(3, 0),(0, 4)]`
Find x and y if `x[(4),(-3)] + y[(-2),(3)] = [(4),(6)]`
If A = `[(2, 5),(4, 3)]`, B = `[(1, -3),(2, 5)]` find AB, BA and verify AB = BA?
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix AT is
If `cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta[(x, -cos theta),(cos theta, x)]` = I2, find x.
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)]`
Consider the matrix Aα = `[(cos alpha, - sin alpha),(sin alpha, cos alpha)]` Find all possible real values of α satisfying the condition `"A"_alpha + "A"_alpha^"T"` = I
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0
Verify the property A(B + C) = AB + AC, when the matrices A, B, and C are given by A = `[(2, 0, -3),(1, 4, 5)]`, B = `[(3, 1),(-1, 0),(4, 2)]` and C = `[(4, 7),(2, 1),(1,-1)]`
If `[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)]` is skew – symmetric find the values of p, q and r
A shopkeeper in a Nuts and Spices shop makes gift packs of cashew nuts, raisins and almonds. Pack I contains 100 gm of cashew nuts, 100 gm of raisins and 50 gm of almonds. Pack-II contains 200 gm of cashew nuts, 100 gm of raisins and 100 gm of almonds. Pack-III contains 250 gm of cashew nuts, 250 gm of raisins and 150 gm of almonds. The cost of 50 gm of cashew nuts is ₹ 50, 50 gm of raisins is ₹ 10, and 50 gm of almonds is ₹ 60. What is the cost of each gift pack?
Choose the correct alternative:
If aij = (3i – 2j) and A = [aij]3 × 2 is
Choose the correct alternative:
If the square of the matrix `[(alpha, beta),(γ, - alpha)]` is the unit matrix of order 2, then α, β, and γ should
Let A = `((1, -1, 0),(0, 1, -1),(0, 0, 1))` and B = 7A20 – 20A7 + 2I, where I is an identity matrix of order 3 × 3. If B = [bij], then b13 is equal to ______.
