Advertisements
Advertisements
प्रश्न
If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?
उत्तर
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
संबंधित प्रश्न
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.
If `[[3x,7],[-2,4]]=[[8,7],[6,4]]`, find the value of x
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
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 aij are given by:
`a_(ij)=|2_i - 3_i|/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 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)= (i-j)/(i+j )`
Given an example of
a triangular matrix
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.
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 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 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 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.
Find a matrix A such that 2A − 3B + 5C = 0, where B =`[(-2, 2, 0), (3, 1, 4)] and "C" = [(2, 0, -2),(7, 1, 6)]`.