Advertisements
Advertisements
प्रश्न
Answer the following question:
Find matrices A and B, where 3A – B = `[(-1, 2, 1),(1, 0, 5)]` and A + 5B = `[(0, 0, 1),(-1, 0, 0)]`
उत्तर
Given equations are
3A – B = `[(-1, 2, 1),(1, 0, 5)]` ...(i)
and A + 5B = `[(0, 0, 1),(-1,0, 0)]` ...(ii)
By (i) × 5 + (ii), we get
16A = `5[(-1, 2, 1),(1, 0, 5)] + [(0, 0, 1),(-1, 0, 0)]`
= `[(-5, 10, 5),(5, 0, 25)] + [(0, 0, 1),(-1, 0, 0)]`
∴ 16A = `[(-5, 10, 6),(4, 0, 25)]`
∴A = `1/16[(-5, 10, 6),(4, 0, 25)]`
By (i) – (ii) × 3, we get
–16B = `[(-1, 2, 1),(1, 0, 5)] -3[(0, 0, 1),(-1, 0, 0)]`
= `[(-1, 2, 1),(1, 0, 5)] - [(0, 0, 3),(-3, 0, 0)]`
∴ –16B = `[(-1, 2, -2),(4, 0, 5)]`
∴ B = `(-1)/16 [(-1, 2, -2),(4, 0, 5)]`
∴ B = `1/16 [(1, -2, 2),(-4, 0, -5)]`
APPEARS IN
संबंधित प्रश्न
Find the values of x and y if
`2 [(x,5),(7,y-3)] [(3,-4),(1,2)] = [(7,6),(15,14)]`
Solve the following equations by reduction method:
x+ y+z = 6,
3x-y+3z = 10
5x+ y-4z = 3
Find x , y , z , w if `[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`
If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` ,
verify that A (adj A) = (adj A) A = |A| . I
A computers centre has four expert programmers . The centre needs four application programmes to be developed. The head of the computer centre , after stying carefully the programmes to be developed , estimates the computer time in minutes required by the respective experts to develop the application programmes as follows :
| Programmes | ||||
| Programmes | 1 | 2 | 3 | 4 |
| (Times in minutes) | ||||
| A | 120 | 100 | 80 | 90 |
| B | 80 | 90 | 110 | 70 |
| C | 110 | 140 | 120 | 100 |
| D | 90 | 90 | 80 | 90 |
How should the head of the computer centre assign the programmes to the programmers so that the total time required is minimum ?
If A = `[(1, -2),(5, 3)], "B" = [(1, -3),(4, -7)]` , then find the matrix A − 2B + 6I, where I is the unit matrix of order 2.
If A = `[(1, 2, -3),(-3, 7, -8),(0, -6, 1)], "B" = [(9, -1, 2),(-4, 2, 5),(4, 0, -3)]` then find the matrix C such that A + B + C is a zero matrix.
If A = `[(1, -2),(3, -5),(-6, 0)],"B" = [(-1, -2),(4, 2),(1, 5)] "and C" = [(2, 4),(-1, -4),(-3, 6)]`, find the matrix X such that 3A – 4B + 5X = C.
If A = `[(5, 1, -4),(3, 2, 0)]`, find (AT)T.
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, find (AT)T.
For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither.
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric, or neither.
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
Solve the following equations for X and Y, if 3X − Y = `[(1, -1),(-1, 1)]` and X – 3Y = `[(0, -1),(0, -1)]`.
There are two book shops own by Suresh and Ganesh. Their sales ( in Rupees) for books in three subject - Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B. July sales ( in Rupees) :
Physics Chemistry Mathematics
A = `[(5600, 6750, 8500),(6650, 7055, 8905)][("Suresh"), ("Ganesh")]`
August Sales (in Rupees :
B = `[(6650, 7055, 8905),(7000, 7500, 10200)][("Suresh"), ("Ganesh")]`
If both book shops get 10% profit in the month of August 2017, find the profit for each book seller in each subject in that month.
If A = `[(1, 2),(-1, -2)], "B" = [(2, "a"),(-1, "b")]` and (A + B)2 = A2 + B2, find the values of a and b.
Find AT, if A = `[(2, -6, 1),(-4, 0, 5)]`
If A = `[(5, -3),(4, -3),(-2, 1)]`, prove that (AT)T = A.
If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, prove that AT = A.
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(2, 1),(4, -1),(-3, 3)], "C" = [(1, 2),(-1, 4),(-2, 3)]`, then show that (A – C)T = AT – CT.
If A = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find AT + 4BT.
If A = `[(-1, 2, 1),(-3, 2, -3)]` and B = `[(2, 1),(-3, 2),(-1, 3)]`, prove that (A + BT)T = AT + B.
Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(1, 2, 4),(3, 2, 1),(-2, -3, 2)]`
Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(5, 2, -4),(3, -7, 2),(4, -5, -3)]`
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (BA)T = ATBT.
Choose the correct alternative.
If A = `[(α, 4),(4, α)]` and |A3| = 729, then α = ______.
Fill in the blank :
If A = `[(4, x),(6, 3)]` is a singular matrix, then x is _______
Solve the following :
Find x, y, z if `[(2, x, 5),(3, 1, z),(y, 5, 8)]` is a symmetric matrix.
Find a, b, c if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.
If A = `[(1, -2),(3, -5),(-6, 0)], "B" = [(-1, -2),(4, 2),(1, 5)] and "C" = [(2, 4),(-1, -4),(-3, 6)]`, find the matrix X such that 3A – 4B + 5X = C.
Find matrices A and B, if `2"A" - "B" = [(6, -6, 0),(-4, 2, 1)] and "A" - 2"B" = [(3, 2, 8),(-2, 1, -7)]`
Simplify, `costheta[(costheta, sintheta),(-sintheta, costheta)] + sintheta[(sintheta, -costheta),(costheta, sintheta)]`
If A = `[("i", 2"i"),(-3, 2)] and "B" = [(2"i", "i"),(2, -3)]`, where `sqrt(-1)` = i,, find A + B and A – B. Show that A + B is a singular. Is A – B a singular ? Justify your answer.
If = `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.
There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subject – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.
July sales (in Rupees), Physics Chemistry Mathematics.
A = `[(5600, 6750, 8500),(6650, 7055, 8905)]"First Row Suresh"/"Second Row Ganesh"`
August sales(in Rupees), Physics Chemistry Mathematics
B = `[(6650, 7055, 8905),(7000, 7500, 10200)]"First Row Suresh"/"Second Row Ganesh"` then,
Find the increase in sales in Rupees from July to August 2017.
In a Skew symmetric matrix, all diagonal elements are ______
If A = `[(2, 5),(1, 3)]` then A–1 = ______.
