Advertisements
Advertisements
Question
If \[A = \begin{bmatrix}2 & - 1 & 3 \\ - 4 & 5 & 1\end{bmatrix}\text{ and B }= \begin{bmatrix}2 & 3 \\ 4 & - 2 \\ 1 & 5\end{bmatrix}\] then
Options
only AB is defined
only BA is defined
AB and BA both are defined
AB and BA both are not defined
Solution
Given :
Order of A is 2 × 3 and order of B is 3 × 2.
Therefore, AB and BA both are defined.
Hence, the correct option is (c).
APPEARS IN
RELATED QUESTIONS
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find AB
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find BA
Compute the indicated product.
`[(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]`
Show that AB ≠ BA in each of the following cases:
`A=[[1 3 0],[1 1 0],[4 1 0]]`And B=`[[0 1 0],[1 0 0],[0 5 1]]`
Compute the products AB and BA whichever exists in each of the following cases:
`A= [[1 -2],[2 3]]` and B=`[[1 2 3],[2 3 1]]`
Compute the products AB and BA whichever exists in each of the following cases:
A = [1 −1 2 3] and B=`[[0],[1],[3],[2]]`
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 [1 −1 x] `[[0 1 -1],[2 1 3],[1 1 1]] [[0],[1],[1]]=`= 0, find x.
Show that the matrix \[A = \begin{bmatrix}5 & 3 \\ 12 & 7\end{bmatrix}\] is root of the equation A2 − 12A − I = O
If \[A = \begin{bmatrix}3 & - 5 \\ - 4 & 2\end{bmatrix}\] , find A2 − 5A − 14I.
\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix}\]show that A2 − 5A + 7I = O use this to find A4.
If `A=[[1,1],[0,1]] ,` Prove that `A=[[1,n],[0,1]]` for all positive integers n.
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).
Give examples of matrices
A and B such that AB = O but BA ≠ O.
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that
(AB)T = BT AT
write AB.
Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.
If \[A = \begin{bmatrix}\cos x & - \sin x \\ \sin x & \cos x\end{bmatrix}\] , find AAT
If A = [aij] is a 2 × 2 matrix such that aij = i + 2j, write A.
For any square matrix write whether AAT is symmetric or skew-symmetric.
If I is the identity matrix and A is a square matrix such that A2 = A, then what is the value of (I + A)2 = 3A?
What is the total number of 2 × 2 matrices with each entry 0 or 1?
For a 2 × 2 matrix A = [aij] whose elements are given by
If \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & - 1\end{bmatrix}\] , then A2 is equal to ___________ .
If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
If S = [Sij] is a scalar matrix such that sij = k and A is a square matrix of the same order, then AS = SA = ?
If A = [aij] is a scalar matrix of order n × n such that aii = k, for all i, then trace of A is equal to
(a) nk (b) n + k (c) \[\frac{n}{k}\] (d) none of these
The matrix \[A = \begin{bmatrix}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{bmatrix}\] is a
The number of possible matrices of order 3 × 3 with each entry 2 or 0 is
If \[A = \begin{pmatrix}\cos\alpha & - \sin\alpha & 0 \\ \sin\alpha & \cos\alpha & 0 \\ 0 & 0 & 1\end{pmatrix},\] ,find adj·A and verify that A(adj·A) = (adj·A)A = |A| I3.
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'` .
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:
- How many articles (in total) are sold by three 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 ______.
