Advertisements
Advertisements
Question
Construct a 4 × 3 matrix whose elements are
aij = i
Solution
`a_(ij)=i`
Here,
`a_11=1,`
`a_12=1`
`a_13=1`
`a_21=2`
`a_22=2`
`a_23=2`
`a_31=3`
`a_31=3`
`a_33=3`
`a_41=4`
`a_42=4`
and
`a_43=4`
So, the required matrix is `[[1 1 1],[2 2 2],[3 3 3],[4 4 4]]`
APPEARS IN
RELATED QUESTIONS
If `A=[[2,0,1],[2,1,3],[1,-1,0]]` , find A2 − 5 A + 16 I.
If A= `((1,0,2),(0,2,1),(2,0,3))` and A3 - 6A2 +7A + kI3 = O find k.
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
If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?
Let A be a matrix of order 3 × 4. If R1 denotes the first row of A and C2 denotes its second column, then determine the orders of matrices R1 and C2
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:
`a_(ij)=(i-2_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 = 2i
Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:
aij = j
Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:
`a_(ij)=1/2= -3i + j `
Construct a 4 × 3 matrix whose elements are
`a_(ij)=2_i+ i/j`
Given an example of
a triangular matrix
If `A=[[cos θ, i sinθ],[i sinθ,cosθ]]` then prove by principle of mathematical induction that `A^n=[[cos nθ,i sinθ],[i sin nθ,cos nθ]]` for all `n ∈ N.`
If A = diag (a, b, c), show that An = diag (an, bn, cn) for all positive integer n.
If A is a square matrix, using mathematical induction prove that (AT)n = (An)T for all n ∈ ℕ.
A matrix X has a + b rows and a + 2 columns while the matrix Y has b + 1 rows and a + 3 columns. Both matrices XY and YX exist. Find a and b. Can you say XY and YX are of the same type? Are they equal.
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.
If A is a skew-symmetric matrix and n is an even natural number, write whether An is symmetric or skew symmetric or neither of these two.
If \[\begin{bmatrix}x & 1\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 2 & 0\end{bmatrix} = O\] , find x.
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 `3"A" - "B" = [(5,0),(1,1)] and "B" = [(4,3),(2,5)]`, then find the martix A.
