Advertisements
Advertisements
Question
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(A + B)T = AT + BT = BT + AT
Solution
AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`
AT = `[(4, 5),(-1, 0),(2, 3)]`
(AT)T = `[(4, 5),(-1, 0),(2, 3)]^"T"`
A = `[(4, -1, 2),(5, 0, 3)]`
BT = `[(2, 7),(-1, 5),(1, -2)]`
A + B = `[(4, -1, 2),(5, 0, 3)]+ [(2, -1, 1),(7, 5, -2)]`
A + B = `[(4 + 2, -1 - 1, 2 +1),(5 + 7, + 5, 3 -2)]`
= `[(6, -2, 3),(12, 5, 1)]`
(A + B)T = `[(6, 12),(-2, 5),(3, 1)]` .......(1)
AT + BT = `[(4, 5),(-1, 0),(2, 3)] [(2, 7),(-1, 5),(1, -2)]`
= `[(4 + 2, 5 +7),(-1 - 1, 0 + 5),(2 + 1, 3 - 2)]`
(A + B)T = `[(6, 12),(-2, 5),(3, 1)]` .......(2)
BT + AT = `[(2, 7),(-1, 5),(1, -2)] + [(4, 5),(-1, 0),(2, 3)]`
= `[(2 + 4, 7 + 5),(-1 - 1, 5 + 0),(1 + 2, -2 + 3)]`
BT + AT = `[(6, 12),(-2, 5),(3, 1)]` .......(3)
From eqution (1), (2) and (3)
(A + B)T = AT + BT = BT + AT
APPEARS IN
RELATED QUESTIONS
If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?
Construct a 3 × 3 matrix whose elements are given by aij = `("i" + "j")^3/3`
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + (– A) = (– A) + A = 0
Find the values of x, y, z if `[(x), (y – z), (z + 3)] + [(y), (4), (3)] = [(4), (8), (16)]`
Solve for x, y : `[(x^2),(y^2)] + 2[(-2x),(-y)] = [(5),(8)]`
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 = `[(costheta, sintheta),(-sintheta, costheta)]` prove that AAT = I
Which of the following can be calculated from the given matrices A = `[(1, 2),(3, 4),(5, 6)]`, B = `[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`,
(i) A2
(ii) B2
(iii) AB
(iv) BA
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)]`
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 and BA ≠ 0
If A is a 3 × 4 matrix and B is a matrix such that both ATB and BAT are defined, what is the order of the matrix B?
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
Choose the correct alternative:
If a ≠ b, b, c satisfy `|("a", 2"b", 2"c"),(3, "b", "c"),(4, "a", "b")|` = 0, then abc =
A matrix is an ordered:-
Let A = [aij] be a square matrix of order 3 such that aij = 2j – i, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + ... + A10 is equal to ______.
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 ______.
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 ______.
