Advertisements
Advertisements
प्रश्न
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" + "j")^3)/5`
Advertisements
उत्तर
A = [aij]3 × 2 = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]`
Given that aij = `(("i" + "j")^3)/5`
∴ a11 = `((1 + 1)^3)/5 = 2^3/5 = 8/5`
a12 = `((1 + 2)^3)/5 = 3^3/5 = 27/5`
a21 = `((2 + 1)^3)/5 = 3^3/5 = 27/5`
a22 = `((2 + 2)^3)/5 = 4^3/5 = 64/5`
a31 = `((3 + 1)^3)/5 = 4^3/5 = 64/5`
a32 = `((3 + 2)^3)/5 = 5^3/5 = 125/5`
∴ A = `[(8/5, 27/5),(27/5, 64/5),(64/5, 125/5)] = 1/5[(8, 27),(27,64),(64, 125)]`
APPEARS IN
संबंधित प्रश्न
The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.
State, whether the following statement is true or false. If false, give a reason.
The matrices A2 × 3 and B2 × 3 are conformable for subtraction.
State, whether the following statement is true or false. If false, give a reason.
A column matrix has many columns and only one row.
Solve for a, b and c; if `[(-4, a + 5),(3, 2)] = [(b + 4, 2),(3, c- 1)]`
If A = `[(8, -3)]` and B = `[(4, -5)]`; find B – A
If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find B + C
Wherever possible, write the following as a single matrix.
`[(1, 2),(3, 4)] + [(-1, -2),(1, -7)]`
Wherever possible, write the following as a single matrix.
`[(2, 3, 4),(5, 6, 7)] - [(0, 2, 3),(6, -1, 0)]`
Find x and y from the given equations:
`[(5, 2),(-1, y - 1)] - [(1, x - 1),(2, -3)] = [(4, 7),(-3, 2)]`
Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix Mt. If possible, find M + Mt
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(B . C) . A = B . (C . A)
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A . (B – C) = A . B – A . C
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(A – B) . C = A . C – B . C
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A2 – B2 = (A + B) (A – B)
Classify the following matrix :
`|(800),(521)|`
Classify the following matrix :
`|(1 , 1),(0,9)|`
Find the values of a and b) if [2a + 3b a - b] = [19 2].
If A = `|(5,"r"),("p",7)|` , c and if A + B = (9,7),(5,8) , find the values of p,q,r and s.
If A = `|("p","q"),(8,5)|` , B = `|(3"p",5"q"),(2"q" , 7)|` and if A + B = `|(12,6),(2"r" , 3"s")|` , find the values of p,q,r and s.
Evaluate the following :
`|(0 , 1),(-1 , 2),(-2 , 0)| |(0 , -4 , 0),(3 , 0 , -1)|`
Evaluate the following :
`|(6 , 1),(3 , 1),(2 , 4)| |(1 , -2 , 1),(2 , 1 , 3)|`
If A = `|(1,3),(3,2)|` and B = `|(-2,3),(-4,1)|` find AB
If P =`|(1 , 2),(3 , 4)|` , Q = `|(5 , 1),(7 , 4)|` and R = `|(2 , 1),(4 , 2)|` find the value of P(Q + R)
Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.
Find the adjoint of the matrix `"A" = [(2,-3),(3,5)]`
Solve the following minimal assignment problem :
| Machines | Jobs | ||
| I | II | III | |
| M1 | 1 | 4 | 5 |
| M2 | 4 | 2 | 7 |
| M3 | 7 | 8 | 3 |
If A = `[(1,2,3), (2,k,2), (5,7,3)]` is a singular matrix then find the value of 'k'.
If `"A" = [(1,2,-3),(5,4,0)] , "B" = [(1,4,3),(-2,5,0)]`, then find 2A + 3B.
Using the truth table statement, examine whether the statement pattern (p → q) ↔ (∼ p v q) is a tautology, a contradiction or a contingency.
`[(2 , 7, 8),(-1 , sqrt(2), 0)]`
Let `"M" xx [(1, 1),(0, 2)]` = [1 2] where M is a matrix.
- State the order of matrix M
- Find the matrix M
Given `[(2, 1),(-3, 4)], "X" = [(7),(6)]` the order of the matrix X
The construction of demand line or supply line is the result of using
Suppose determinant of a matrix Δ = 0, then the solution
If a matrix A = `[(0, 1),(2, -1)]` and matrix B = `[(3),(1)]`, then which of the following is possible:
Event A: Order of matrix A is 3 × 5.
Event B: Order of matrix B is 5 × 3.
Event C: Order of matrix C is 3 × 3.
Product of which two matrices gives a square matrix.
