Advertisements
Advertisements
Question
If A is 3 × 4 matrix and B is a matrix such that A'B and BA' are both defined. Then, B is of the type
Options
3 × 4
3 × 3
4 × 4
4 × 3
Solution
3 × 4
The order of A is 3x 4. So, the order of A' is 4x 3
Now, both
`A’B` and `BA’` are defined. So, the number of columns in A' should be equal to the number of rows in B for A'B.
Also, the number of columns in B should be equal to number of rows in A' for BA'.
Hence, the order of matrix B is 3 X 4
APPEARS IN
RELATED QUESTIONS
Write the element a12 of the matrix A = [aij]2 × 2, whose elements aij are given by aij = e2ix sin jx.
Find the maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`
Write the element a23 of a 3 ✕ 3 matrix A = (aij) whose elements aij are given by `a_(ij)=∣(i−j)/2∣`
If `[[3x,7],[-2,4]]=[[8,7],[6,4]]`, find the value of x
Construct a 2 × 2 matrix whose elements `a_(ij)`
are given by: `(i+j)^2/2`
Construct a 2 × 2 matrix whose elements aij are given by:
`aij=(i-j)^2/2`
Construct a 2 × 2 matrix whose elements aij are given by:
`a_(ij)=(i-2_j)^2/2`
Construct a 2 × 2 matrix whose elements aij are given by:
`a_(ij)= (2i +j)^2/2`
Construct a 2 × 2 matrix whose elements aij are given by:
`a_(ij)=|2_i - 3_i|/2`
Construct a 2 × 2 matrix whose elements aij are given by:
`a_(ij)=|-3i +j|/2`
Construct a 2 × 2 matrix whose elements aij are given by:
`a_(ij)=e^(2ix) sin (xj)`
Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:
aij = i + j
Construct a 3 × 4 matrix A = [ajj] whose elements ajj are given by:
ajj = i − j
Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:
aij = 2i
Construct a 4 × 3 matrix whose elements are
`a_(ij)=2_i+ i/j`
Construct a 4 × 3 matrix whose elements are
`a_(ij)= (i-j)/(i+j )`
Construct a 4 × 3 matrix whose elements are
aij = i
Given an example of
a triangular matrix
If A and B are symmetric matrices, then write the condition for which AB is also symmetric.
If B is a skew-symmetric matrix, write whether the matrix AB AT is symmetric or skew-symmetric.
If B is a symmetric matrix, write whether the matrix AB AT is symmetric or skew-symmetric.
If A is a skew-symmetric and n ∈ N such that (An)T = λAn, write the value of λ.
If A is a symmetric matrix and n ∈ N, write whether An is symmetric or skew-symmetric or neither of these two.
Matrix A = \[\begin{bmatrix}0 & 2b & - 2 \\ 3 & 1 & 3 \\ 3a & 3 & - 1\end{bmatrix}\] is given to be symmetric, find values of a and b.
`If A = ([3 5] , [7 9])` is written as A = P + Q, where as A = p + Q , Where P is a symmetric matrix and Q is skew symmetric matrix , then wqrite the matrix P.
Let A and B be matrices of orders 3 x 2 and 2 x
4 respectively. Write the order of matrix AB.
If the matrix AB is zero, then
If \[A = \begin{bmatrix}5 & x \\ y & 0\end{bmatrix}\] and A = AT, then
If \[A = \begin{bmatrix}\cos \theta & - \sin \theta \\ \sin \theta & \cos \theta\end{bmatrix}\] then AT + A = I2, if
If `3"A" - "B" = [(5,0),(1,1)] and "B" = [(4,3),(2,5)]`, then find the martix A.
