Advertisements
Advertisements
प्रश्न
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that (A – B)T = AT – BT
उत्तर
A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]`
A – B = `[(1, 2),(1, 3)] - [(4, 0),(1, 5)]`
= `[(-3, 2),(0, 2)]`
(A – B)T = `[(-3, 0),(2, -2)]` ...(1)
AT = `[(1, 1),(2, 3)]`
BT = `[(4, 1),(0, 5)]`
AT – BT = `[(1, 1),(2, 3)] - [(4, 1),(0, 5)]`
= `[(-3, 0),(2, -2)]` ...(2)
From (1) and (2) we get
(A – B)T = AT – BT
APPEARS IN
संबंधित प्रश्न
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of B – 5A
If A = `[(costheta, sintheta),(-sintheta, costheta)]` prove that AAT = I
Construct an m × n matrix A = [aij], where aij is given by
aij = `("i" - 2"j")^2/2` with m = 2, n = 3
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 3 × 4 matrix and B is a matrix such that both ATB and BAT are defined, what is the order of the matrix B?
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:
`[(4, -2),(3, -5)]`
If A and B are symmetric matrices of same order, prove that AB + BA is a symmetric matrix
Choose the correct alternative:
Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?
Let A = `[(cosα, -sinα),(sinα, cosα)]`, α ∈ R such that A32 = `[(0, -1),(1, 0)]`. Then a value of α is ______.
If A = `[(1, 2),(2, 3)]` and A2 – kA – I2 = 0, then value of k is ______.
