Advertisements
Advertisements
प्रश्न
Find the maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`
उत्तर
`"Let "Delta = |(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`
Applying R2 → R2 - R1 and R3 → R3 - R1, we get
`Delta=|(1,1,1),(0,sintheta,0),(0,0,costheta)|`
`Delta=sinthetacostheta`
`Delta=(sin2theta)/2`
We know that -1 ≤ sin2θ ≤ 1
∴ Maximum value of `Delta =1/2 xx 1 = 1/2`
APPEARS IN
संबंधित प्रश्न
If `A=[[2,0,1],[2,1,3],[1,-1,0]]` , find A2 − 5 A + 16 I.
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.
If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?
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:
`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 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:
`a_(ij)=1/2= -3i + j `
Construct a 4 × 3 matrix whose elements are
`a_(ij)=2_i+ i/j`
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.
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 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.
Let A and B be matrices of orders 3 x 2 and 2 x
4 respectively. Write the order of matrix AB.
If `3"A" - "B" = [(5,0),(1,1)] and "B" = [(4,3),(2,5)]`, then find the martix A.
