Advertisements
Advertisements
प्रश्न
Fill in the blank :
If A = `[(4, x),(6, 3)]` is a singular matrix, then x is _______
उत्तर
|A| = 0
∴ `|(4, x),(6, 3)|` = 0
∴ 12 – 6x = 0
∴ x = 2.
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)]`
Find x , y , z , w if `[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`
Simplify the following :
`{3 [(1,2,0),(0,-1,3)] - [(1,5,-2),(-3,-4,4)]} [(1),(2),(1)]`
If A = `[(1,2,3),(2,"a",2),(5,7,3)]` is a singular matrix , find the value of 'a'.
Solve the following equations by reduclion method
x+3y+3z= 16 , x+4y+4z=21 , x+3y+4z = 19
Solve the following equations by reduction method :
x + 2y + z = 8
2x+ 3y - z = 11
3x - y - 2z = 5
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 = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2),(0, 3)] "and C" = [(4, 3),(-1, 4),(-2, 1)]`, Show that (A + B) + C = A + (B + C)
If A = `[(5, 1, -4),(3, 2, 0)]`, 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.
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
Solve the following equations for X and Y, if 3X − Y = `[(1, -1),(-1, 1)]` and X – 3Y = `[(0, -1),(0, -1)]`.
If [aij]3×3, where aij = 2(i – j), find A and AT. State whether A and AT both are symmetric or skew-symmetric matrices?
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 + B)T = AT + BT.
If A = `[(1, 0, 1),(3, 1, 2)], "B" = [(2, 1, -4),(3, 5, -2)] "and" "C" = [(0, 2, 3),(-1, -1, 0)]`, verify that (A + 2B + 3C)T = AT + 2BT + CT.
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)]`
Solve the following :
Find x, y, z if `[(2, x, 5),(3, 1, z),(y, 5, 8)]` is a symmetric matrix.
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2), (0, 3)] and "C" = [(4, 3),(-1, 4),(-2, 1)]` Show that A + B = B + A
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2), (0, 3)] and "C" = [(4, 3),(-1, 4),(-2, 1)]` Show that (A + B) + C = A + (B + 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.
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,
If both book shops got 10 % profit in the month of August 2017, find the profit for each book seller in each subject in that month
Evaluate: `[(3),(2),(1)][(2,-4,3)]`
Evaluate : `[2 -1 3][(4),(3),(1)]`
Answer the following question:
Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`
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)]`
Choose the correct alternative:
For any square matrix B, matrix B + BT is ______
Choose the correct alternative:
If A and B are two square matrices of order 3, then (AB)T = ______
State whether the following statement is True or False:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]` is a skew symmetric matrix
If A = `[(2, 5),(1, 3)]` then A–1 = ______.
If A = `[(5, 4),(-2, 3)]` and B = `[(-1, 3),(4, -1)]`, then find CT , such that 3A – 2B + C = I, where I is the unit matrix of order 2
