Advertisements
Advertisements
Question
Find the maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`
Solution
`"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
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∣`
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 `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)=|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 = [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 4 × 3 matrix whose elements are
`a_(ij)= (i-j)/(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 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 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 matrix and n is an even natural number, 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 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
