Advertisements
Advertisements
प्रश्न
Find x, if `[(1, "x", 1)][(1, 2, 3),(4, 5, 6),(3, 2, 5)] [(1),(-2), (3)]` = 0
Advertisements
उत्तर
`[(1, "x", 1)][(1, 2, 3),(4, 5, 6),(3, 2, 5)] [(1),(-2), (3)]` = 0
∴ `[(1, "x", 1)] [(1 - 4 + 9),(4 - 10 + 18),(3 - 4 + 15)]` = 0
∴ `[(1, "x", 1)] [(6),(12),(14)]` = 0
∴ [6 + 12x + 14] = [0]
∴ by equality of matrices, 12x + 20 = 0
∴ x = `-5/3`.
APPEARS IN
संबंधित प्रश्न
If A = `[(1, -3),(4, 2)], "B" = [(4, 1),(3, -2)]` show that AB ≠ BA.
If A = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)], "B" = [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`. State whether AB = BA? Justify your answer.
Show that AB = BA where,
A = `[(costheta, - sintheta),(sintheta, costheta)], "B" = [(cosphi, -sinphi),(sinphi, cosphi)]`
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 A(BC) = (AB)C of the following case:
A = `[(2, 4, 3),(-1, 3, 2)], "B" = [(2, -2),(3, 3),(-1, 1)], "C" = [(3, 1),(1, 3)]`
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 = `[(1, -2),(5, 6)], "B" = [(3, -1),(3, 7)]`, Find AB - 2I, where I is unit matrix of order 2.
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
If A = `[(3, 4),(-4, 3)] and "B" = [(2, 1),(-1, 2)]`, show that (A + B)(A – B) = A2 – B2
Find matrix X such that AX = B, where A = `[(1, -2),(-2, 1)]` and B = `[(-3),(-1)]`
Find k, if A= `[(3, -2),(4, -2)]` and if A2 = kA – 2I
Find x and y, if `{4[(2, -1, 3),(1, 0, 2)] -[(3, -3, 4),(2, 1, 1)]} [(2),(-1),(1)] = [(x),(y)]`
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that `"A"^2=[(cos2alpha, sin2alpha),(-sin2alpha, cos2alpha)]`
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 A + B = `[(7, 4),(8, 9)]` and A − B = `[(1, 2),(0, 3)]` then the value of A is _______
Select the correct option from the given alternatives:
If A = `[(-2, 1),(0, 3)]` and f(x) = 2x2 – 3x, then f(A) = ………
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 = `[(2, -2, -4),(-1, 3, 4),(1, -2, -3)]` show that A2 = A
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:
If A = `[(2, -1),(3, -2)]`, find A3
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:
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
