Advertisements
Advertisements
प्रश्न
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = i – 3j
Advertisements
उत्तर
A = [aij]3 × 2 = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]`
aij = i – 3j
∴ a11 = 1 – 3(1) = 1 – 3 = –2,
a12 = 1 – 3(2) = 1 – 6 = –5,
a21 = 2 – 3(1) = 2 – 3 = –1,
a22 = 2 – 3(2) = 2 – 6 = – 4
a31 = 3 – 3(1) = 3 – 3 = 0,
a32 = 3 – 3(2) = 3 – 6 = –3
∴ A = `[(-2, -5),(-1, -4),(0, -3)]`
APPEARS IN
संबंधित प्रश्न
State, whether the following statement is true or false. If false, give a reason.
If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.
State, whether the following statement is true or false. If false, give a reason.
Transpose of a square matrix is a square matrix.
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 = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A – 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)]`
Wherever possible, write the following as a single matrix.
`[(0, 1, 2),(4, 6, 7)] + [(3, 4),(6, 8)]`
Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix Mt. If possible, find Mt – M
Evaluate:
`2[(-1 0)/(2 -3)] +[(3 3)/(5 0)]`
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
Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.
Classify the following rnatrix :
`|(2,1),(0 , 6),(8 , 7) |`
Classify the following matrix :
`|(800),(521)|`
Classify the following matrix :
`|(1 , 1),(0,9)|`
Classify the following matrix :
`|(11 , 3 , 0),(21 , 8 , 4),(15,5,2)|`
If P= (8,5),(7,2) find : P + Pt
If P = `|(8,5),(7,2)|` find P - Pt
Evaluate the following :
`|(2 , 3),(-4 , 0)| |(3 , -2),(-1 , 4)|`
Evaluate the following :
`|(6 , 1),(3 , 1),(2 , 4)| |(1 , -2 , 1),(2 , 1 , 3)|`
Evaluate the following :
`|(0 , 1 , 0),(2 , 0 , -3),(1 , 0 , -2)| |(1 , -2),(3 , 4),(0 , 0)|`
If A = `|(1,3),(3,2)|` and B = `|(-2 , 3),(-4 , 1)|` find BA
If A = `[(2, 3), (1, 2)], B = [(1, 0),(3, 1)]`, Find (AB)-1
Solve the equation x + y = 4 and 2x - y = 5 using the method of reduction.
Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.
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 = `[(7,1), (2,5)]` and B = `[(1,2), (3,-1)]` then verify that |AB| = |A| |B|.
If A = `[(1,0,0),(2,1,0),(3,3,1)]` then find A-1 by using elementary transformation .
`[(2, -1),(5, 1)]`
[2 3 – 7]
`[(2 ,- 4),(0 ,0),(1 , 7)]`
`[(0, 0, 0),(0, 0, 0)]`
If a matrix has 4 elements, what are the possible order it can have?
If a matrix has 8 elements, what are the possible order it can have?
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" - "j")^2)/(5 - "i")`
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" + "j")^3)/5`
If A is a matrix of order m × 3, B is a matrix of order 3 × 2 and R is a matrix of order 5 × n such that AB = R, the value of m and n are ______.
