Advertisements
Advertisements
Question
If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?
Solution
We know that if a matrix is of order `m xx n` then it has mn elements.
The possible orders of a matrix with 8 elements are given below:
1 x 8, 2 x 4, 4 x 2 , 8 x 1
Thus, there are 4 possible orders of the matrix.
The possible orders of a matrix with 5 elements are given below:
1 x 5, 5 x 1
Thus, there are 2 possible orders of the matrix.
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.
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 = [aij] =`[[2,3,-5],[1,4,9],[0,7,-2]]`and B = [bij] `[[2,-1],[-3,4],[1,2]]`
then find (i) a22 + b21 (ii) a11 b11 + a22 b22
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)=|2_i - 3_i|/2`
Construct a 2 × 2 matrix whose elements aij are given by:
`a_(ij)=|-3i +j|/2`
Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:
aij = i + j
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
aij = i
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 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.
The cooperative stores of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs. 8.30, Rs. 3.45 and Rs. 4.50 each respectively. Find the total amount the store will receive from selling all the items.
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 the matrix AB is zero, then
If \[A = \begin{bmatrix}5 & x \\ y & 0\end{bmatrix}\] and A = AT, then
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
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.
