Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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 number of elements
If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + (– A) = (– A) + A = 0
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of B – 5A
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?
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
If A = `[(3, 1),(-1, 2)]` show that A2 – 5A + 7I2 = 0
If the number of columns and rows are not equal in a matrix then it is said to be a
Transpose of a column matrix is
A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]` find the matrix D, such that CD – AB = 0
Determine the value of x + y if `[(2x + y, 4x),(5x - 7, 4x)] = [(7, 7y - 13),(y, x + 6)]`
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
Show that f(x) f(y) = f(x + y), where f(x) = `[(cosx, -sinx, 0),(sinx, cosx, 0),(0, 0, 1)]`
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
If A and B are symmetric matrices of same order, prove that AB – BA is a skew-symmetric matrix
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:
What must be the matrix X, if `2"X" + [(1, 2),(3, 4)] = [(3, 8),(7, 2)]`?
Choose the correct alternative:
If a ≠ b, b, c satisfy `|("a", 2"b", 2"c"),(3, "b", "c"),(4, "a", "b")|` = 0, then abc =
Let P = `[(3, -1, -2),(2, 0, alpha),(3, -5, 0)]`, where α ∈ R. Suppose Q = [qij] is a matrix satisfying PQ = kI3 for some non-zero k ∈ R. If q23 = `-k/8` and |Q| = `k^2/2`, then α2 + k2 is equal to ______.
