Advertisements
Advertisements
Question
If A = `[[3,9,0] ,[1,8,-2], [7,5,4]]` and B =`[[4,0,2],[7,1,4],[2,2,6]]` , then find the matrix `B'A'` .
Solution
B' = `[[4,7,2],[0,1,2],[2,4,6]]` & A' = `[[3,1,7],[9,8,5],[0,-2,4]]`
`therefore` B'A' = `[[4,7,2],[0,1,2],[2,4,6]][[3,1,7],[9,8,5],[0,-2,4]]`
= `[[12+63, 4+56-4, 28+35+8],[9,8-4,5+8],[6+36,2+32-12,14+20+24]]`
= `[[75,56,71],[9,4,13],[42,22,58]]`
APPEARS IN
RELATED QUESTIONS
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find AB
Compute the indicated products:
`[[1 -2],[2 3]][[1 2 3],[-3 2 -1]]`
Compute the products AB and BA whichever exists in each of the following cases:
[a, b]`[[c],[d]]`+ [a, b, c, d] `[[a],[b],[c],[d]]`
If A =
\[\begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\]and B =
\[\begin{bmatrix}- 1 & 3 & 5 \\ 1 & - 3 & - 5 \\ - 1 & 3 & 5\end{bmatrix}\] , show that AB = BA = O3×3.
If A =`[[2 -3 -5],[-1 4 5],[1 -3 -4]]` and B =`[[2 -2 -4],[-1 3 4],[1 2 -3]]`
, show that AB = A and BA = B.
Let A =`[[-1 1 -1],[3 -3 3],[5 5 5]]`and B =`[[0 4 3],[1 -3 -3],[-1 4 4]]`
, compute A2 − B2.
If
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 , then show that A is a root of the polynomial f (x) = x3 − 6x2 + 7x + 2.
Find the matrix A such that [2 1 3 ] `[[-1,0,-1],[-1,1,0],[0,1,1]] [[1],[0],[-1]]=A`
If `A=[[0,-x],[x,0]],[[0,1],[1,0]]` and `x^2=-1,` then show that `(A+B)^2=A^2+B^2`
If B, C are n rowed square matrices and if A = B + C, BC = CB, C2 = O, then show that for every n ∈ N, An+1 = Bn (B + (n + 1) C).
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.
A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interes. Using matrix method, find the amount invested by the trust.
Write matrix A satisfying ` A+[[2 3],[-1 4]] =[[3 6],[- 3 8]]`.
If \[A = \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix}\] is identity matrix, then write the value of α.
If \[\begin{bmatrix}\cos\frac{2\pi}{7} & - \sin\frac{2\pi}{7} \\ \sin\frac{2\pi}{7} & \cos\frac{2\pi}{7}\end{bmatrix}^k = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\] then the least positive integral value of k is _____________.
If \[A = \begin{bmatrix}\alpha & \beta \\ \gamma & - \alpha\end{bmatrix}\] is such that A2 = I, then
If A and B are square matrices of the same order, then (A + B)(A − B) is equal to
If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find A matrix Z such that X + Y + Z is a zero matrix
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A(BC) = (AB)C
The matrix P = `[(0, 0, 4),(0, 4, 0),(4, 0, 0)]`is a ______.
If A, B and C are square matrices of same order, then AB = AC always implies that B = C
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:
- If the number of handmade fans and plates are interchanged for all the schools, then what is the total money collected by all schools?
Let a, b, c ∈ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = `((a, b, c),(b, c, a),(c, a, b))` satisfies ATA = I, then a value of abc can be ______.
