Advertisements
Advertisements
प्रश्न
Construct a 2 × 2 matrix whose elements aij are given by:
`a_(ij)=e^(2ix) sin (xj)`
उत्तर
`a_(ij)=e^(2ix) sin (xj)`
Here,
`a_11=e^(2xx1xxx)sin(x xx1)= e^(2x) sin(x), a_12= e^(2xx1xxx) sin (x xx 2)= e^(2x) sin (2x)`
`a_21= e^(2 xx 2xx x)sin (x xx 1)= e^(4x) sin (x) , a_22 = e^(2 xx 2xx x) sin (x xx 2)= 6^(4x)sin (2x)`
So, the required matrix is `[[e^(2x)sin (x) e^(2x)sin (2x)],[e^(4x)sin (x) e^(4x)sin (2x)]]`
APPEARS IN
संबंधित प्रश्न
Write the element a12 of the matrix A = [aij]2 × 2, whose elements aij are given by aij = e2ix sin jx.
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
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)= (2i +j)^2/2`
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 = [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)=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=[[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.
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 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 odd natural number, write whether An is symmetric or skew-symmetric or neither of the 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 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 `3"A" - "B" = [(5,0),(1,1)] and "B" = [(4,3),(2,5)]`, then find the martix A.
