Advertisements
Advertisements
प्रश्न
If A = `[(1, 2),(-1, -2)], "B" = [(2, "a"),(-1, "b")]` and if (A + B)2 = A2 + B2 . find values of a and b
Advertisements
उत्तर
Since (A + B)2 = A2 + B2,
(A + B)(A + B) = A2 + B2
∴ A2 + AB + BA + B2 = A2 + B2
∴ AB + BA = 0
∴ AB = – BA
∴ `[(1, 2),(-1, -2)] [(2, "a"),(-1, "b")] = -[(2, "a"),(-1, "b")] [(1, 2),(-1, -2)]`
∴ `[(2 - 2, "a" + 2"b"),(-2 + 2, -"a" - 2"b")] = -[(2 - "a", 4 - 2"a"),(-1 - "b", -2 - 2"b")]`
∴ `[(0, "a" + 2"b"),(0, -"a" - 2"b")] = [(-2 + "a", -4 + 2"a"),(1 + "b", 2 + 2"b")]`
∴ by the equality of matrices,
0 = – 2 + a ... (1)
0 = 1 + b ... (2)
a + 2b = – 4 + 2a ... (3)
– a – 2b = 2 + 2b ... (4)
From equations (1) and (2), we get,
a = 2 and b = – 1
Since the values of a and b satisfy equations (3) and (4).
Hence, a = 2 and b = – 1.
APPEARS IN
संबंधित प्रश्न
If A = `[(1, -3),(4, 2)], "B" = [(4, 1),(3, -2)]` show that AB ≠ BA.
Show that AB = BA where,
A = `[(-2, 3, -1),(-1, 2, -1),(-6, 9, -4)], "B" = [(1, 3, -1),(2, 2, -1),(3, 0, -1)]`
Show that AB = BA where,
A = `[(costheta, - sintheta),(sintheta, costheta)], "B" = [(cosphi, -sinphi),(sinphi, cosphi)]`
If A = `[(4, 8),(-2, -4)]`, prove that A2 = 0
Verify A(BC) = (AB)C of the following case:
A = `[(1, 0, 1),(2, 3, 0),(0, 4, 5)], "B" = [(2, -2),(-1, 1),(0, 3)] and "C" = [(3, 2, -1),(2, 0, -2)]`
Verify that A(B + C) = AB + AC of the following matrix:
A = `[(4, -2),(2, 3)], "B" = [(-1, 1),(3, -2)] and "C" = [(4, 1),(2, -1)]`
Verify that A(B + C) = AB + AC of the following matrix:
A = `[(1, -1, 3),(2, 3, 2)], "B" = [(1, 0),(-2, 3),(4, 3)], "C" = [(1, 2),(-2, 0),(4, -3)]`
If A = `[(4, 3, 2),(-1, 2, 0)], "B" = [(1, 2),(-1, 0),(1, -2)]` show that matrix AB is non singular
A = `[(alpha, 0),(1, 1)], "B" = [(1, 0),(2, 1)]` find α, if A2 = B.
If A = `[(8, 4),(10, 5)], "B" = [(5, -4),(10, -8)]` show that (A + B)2 = A2 + AB + B2
Find k, if A= `[(3, -2),(4, -2)]` and if A2 = kA – 2I
Find x, if `[(1, "x", 1)][(1, 2, 3),(4, 5, 6),(3, 2, 5)] [(1),(-2), (3)]` = 0
Find x and y, if `{4[(2, -1, 3),(1, 0, 2)] -[(3, -3, 4),(2, 1, 1)]} [(2),(-1),(1)] = [(x),(y)]`
Find x, y, z if `{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)]` = `[("x" - 3),("y" - 1),(2"z")]`
If A = `[(1, 2),(3, 5)]` B = `[(0, 4),(2, -1)]`, show that AB ≠ BA, but |AB| = IAl·IBI
Jay and Ram are two friends in a class. Jay wanted to buy 4 pens and 8 notebooks, Ram wanted to buy 5 pens and 12 notebooks. Both of them went to a shop. The price of a pen and a notebook which they have selected was Rs.6 and Rs.10. Using Matrix multiplication, find the amount required from each one of them
Select the correct option from the given alternatives:
If `[("x", 3"x" - "y"),("zx" + "z", 3"y" - "w")] = [(3, 2),(4, 7)]` then ______
Answer the following question:
If f(α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(– α)
Answer the following question:
If f (α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(–α) + f(α)
Answer the following question:
If A = `[(3, -5),(-4, 2)]`, show that A2 – 5A – 14I = 0
Answer the following question:
if A = `[(-3, 2),(2, -4)]`, B = `[(1, x),(y, 0)]`, and (A + B)(A – B) = A2 – B2 , find x and y
Answer the following question:
If A = `[(0, 1),(1, 0)]` and B = `[(0, -1),(1, 0)]` show that (A + B)(A – B) ≠ A2 – B2
Answer the following question:
Find x, y if, `[(0, -1, 4)]{2[(4, 5),(3, 6),(2, -1)] + 3[(4, 3),(1, 4),(0, -1)]} = [(x, y)]`
Answer the following question:
Find x, y, z if `{5[(0, 1),(1, 0),(1, 1)] -3[(2, 1),(3, -2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`
Answer the following question:
Find x, y, z if `{[(1, 3, 2),(2, 0, 1),(3, 1, 2)] + 2[(3, 0, 2),(1, 4, 5),(2, 1, 0)]} [(1),(2),(3)] = [(x),(y),(z)]`
Answer the following question:
Two farmers Shantaram and Kantaram cultivate three crops rice,wheat and groundnut. The sale (In Rupees) of these crops by both the farmers for the month of April and may 2008 is given below,
| April sale (In Rs.) | |||
| Rice | Wheat | Groundnut | |
| Shantaram | 15000 | 13000 | 12000 |
| Kantaram | 18000 | 15000 | 8000 |
| May sale (In Rs.) | |||
| Rice | Wheat | Groundnut | |
| Shantaram | 18000 | 15000 | 12000 |
| Kantaram | 21000 | 16500 | 16000 |
Find The total sale in rupees for two months of each farmer for each crop
Which description correctly states matrix multiplication?
For which condition does the product \[AB\] exist?
Which property is an associative property of matrix multiplication?
Which equation shows that matrix multiplication is distributive over addition?
Which equation expresses that the identity matrix acts as a multiplicative identity?
