Advertisements
Advertisements
प्रश्न
Compute the indicated product.
`[(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]`
उत्तर
`[(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]`
`= [(3(2)-1(1)+3(3), 3(-3)-1(0)+3(1)), (-1(2)+0(1)+2(3), -1(-3)+0(0)+2(1))]`
`= [(6-1+9, -9-0+3), (-2+0+6, 3+0+2)]`
`= [(14, -6),(4,5)]`
APPEARS IN
संबंधित प्रश्न
Which of the given values of x and y make the following pair of matrices equal?
`[(3x+7, 5),(y+1, 2-3x)] = [(0,y-2),(8,4)]`
Compute the indicated products:
`[[a b],[-b a]][[a -b],[b a]]`
Evaluate the following:
`[[1 -1],[0 2],[2 3]]` `([[1 0 2],[2 0 1]]-[[0 1 2],[1 0 2]])`
If
If A=then find λ, μ so that A2 = λA + μI
Solve the matrix equations:
[2x 3] `[[1 2],[-3 0]] , [[x],[8]]=0`
If `A= [[1,2,0],[3,-4,5],[0,-1,3]]` compute A2 − 4A + 3I3.
If f (x) = x3 + 4x2 − x, find f (A), where\[A = \begin{bmatrix}0 & 1 & 2 \\ 2 & - 3 & 0 \\ 1 & - 1 & 0\end{bmatrix}\]
`A=[[3,2, 0],[1,4,0],[0,0,5]]` show that A2 − 7A + 10I3 = 0
Find the matrix A such that [2 1 3 ] `[[-1,0,-1],[-1,1,0],[0,1,1]] [[1],[0],[-1]]=A`
If `A=[[1,1],[0,1]] ,` Prove that `A=[[1,n],[0,1]]` for all positive integers n.
If A and B are square matrices of the same order, explain, why in general
(A + B)2 ≠ A2 + 2AB + B2
In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as
Cost per contact
`A=[[40],[100],[50]]` `[["Teliphone"] ,["House call "],[" letter"]]`
The number of contacts of each type made in two cities X and Y is given in matrix B as
Telephone House call Letter
`B= [[ 1000, 500, 5000],[3000,1000, 10000 ]]`
Find the total amount spent by the group in the two cities X and Y.
To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:
(i) ₹50 (ii) ₹20 (iii) ₹40
The number of attempts made in three villages X, Y and Z are given below:
(i) (ii) (iii)
X 400 300 100
Y 300 250 75
Z 500 400 150
Find the total cost incurred by the organisation for three villages separately, using matrices.
There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question?
Write a 2 × 2 matrix which is both symmetric and skew-symmetric.
If `[2 1 3]([-1,0,-1],[-1,1,0],[0,1,1])([1],[0],[-1])=A` , then write the order of matrix A.
If `A=[[i,0],[0,i ]]` , n ∈ N, then A4n equals
If A and B are two matrices such n that AB = B and BA = A , `A^2 + B^2` is equal to
If \[A = \begin{bmatrix}1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} and B = \begin{bmatrix}1 & - 2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\] and AB = I3, then x + y equals
If A is a square matrix such that A2 = A, then (I + A)3 − 7A is equal to
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
The number of possible matrices of order 3 × 3 with each entry 2 or 0 is
If A is a square matrix such that A2 = I, then (A − I)3 + (A + I)3 − 7A is equal to
If A = `[(3, 5)]`, B = `[(7, 3)]`, then find a non-zero matrix C such that AC = BC.
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.
If matrix A = [aij]2×2, where aij `{:(= 1 "if i" ≠ "j"),(= 0 "if i" = "j"):}` then A2 is equal to ______.
If A and B are two square matrices of the same order, then AB = BA.
If A, B and C are square matrices of same order, then AB = AC always implies that B = C
If A `= [(1,-2,1),(2,1,3)]` and B `= [(2,1),(3,2),(1,1)],` then (AB)T is equal
Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as
| School/Article | DPS | CVC | KVS |
| Handmade/fans | 40 | 25 | 35 |
| Mats | 50 | 40 | 50 |
| Plates | 20 | 30 | 40 |
Based on the information given above, answer the following questions:
- What is the total amount of money (in Rs.) collected by schools CVC and KVS?
Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as
| School/Article | DPS | CVC | KVS |
| Handmade/fans | 40 | 25 | 35 |
| Mats | 50 | 40 | 50 |
| Plates | 20 | 30 | 40 |
Based on the information given above, answer the following questions:
- How many articles (in total) are sold by three schools?
If A = `[(1, 1, 1),(0, 1, 1),(0, 0, 1)]` and M = A + A2 + A3 + .... + A20, then the sum of all the elements of the matrix M is equal to ______.
If A = `[(a, b),(b, a)]` and A2 = `[(α, β),(β, α)]`, then ______.
