Advertisements
Advertisements
प्रश्न
Compute the indicated products:
`[[a b],[-b a]][[a -b],[b a]]`
उत्तर
`[[a b],[-b a]][[a -b],[b a]]`
`⇒ [[a xx axx+b+b axx(-b)+bxxa],[(-b)xxa+axxb (-b)xx(-b)+axxa]]`
`⇒[[a^2+b^2 -ab^2+ab],[-ab+ab b^2+a^2]]`
`⇒[[a^2+b^2 0],[0 a^2+b^2]]`
APPEARS IN
संबंधित प्रश्न
Which of the given values of x and y make the following pair of matrices equal?
`[(3x+7, 5),(y+1, 2-3x)] = [(0,y-2),(8,4)]`
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find BA
Compute the indicated product.
`[(1),(2),(3)] [2,3,4]`
Compute the indicated products
`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`
Compute the indicated product.
`[(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]`
Show that AB ≠ BA in each of the following cases:
`A= [[5 -1],[6 7]]`And B =`[[2 1],[3 4]]`
Evaluate the following:
`[[1 -1],[0 2],[2 3]]` `([[1 0 2],[2 0 1]]-[[0 1 2],[1 0 2]])`
If A = `[[ cos 2θ sin 2θ],[ -sin 2θ cos 2θ]]`, find A2.
If A =`[[2 -3 -5],[-1 4 5],[1 -3 -4]]` and B =`[[2 -2 -4],[-1 3 4],[1 2 -3]]`
, show that AB = A and BA = B.
For the following matrices verify the associativity of matrix multiplication i.e. (AB) C = A(BC):
`A =-[[1 2 0],[-1 0 1]]`,`B=[[1 0],[-1 2],[0 3]]` and C= `[[1],[-1]]`
For the following matrices verify the distributivity of matrix multiplication over matrix addition i.e. A (B + C) = AB + AC:
`A = [[1 -1],[0 2]] B= [[-1 0],[2 1]]`and `C= [[0 1],[1 -1]]`
If \[A = \begin{bmatrix}4 & - 1 & - 4 \\ 3 & 0 & - 4 \\ 3 & - 1 & - 3\end{bmatrix}\] , Show that A2 = I3.
If
If A=, find k such that A2 = kA − 2I2
If\[A = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix}\] f (x) = x2 − 2x − 3, show that f (A) = 0
Solve the matrix equations:
`[x1][[1,0],[-2,-3]][[x],[5]]=0`
Solve the matrix equations:
`[[],[x-5-1],[]][[1,0,2],[0,2,1],[2,0,3]] [[x],[4],[1]]=0`
If `A= [[1,2,0],[3,-4,5],[0,-1,3]]` compute A2 − 4A + 3I3.
Find the matrix A such that [2 1 3 ] `[[-1,0,-1],[-1,1,0],[0,1,1]] [[1],[0],[-1]]=A`
Let `A=[[1,1,1],[3,3,3]],B=[[3,1],[5,2],[-2,4]]` and `C=[[4,2],[-3,5],[5,0]]`Verify that AB = AC though B ≠ C, A ≠ O.
Three shopkeepers A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs. 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual's bill.
In a parliament election, a political party hired a public relations firm to promote its candidates in three ways − telephone, house calls and letters. The cost per contact (in paisa) is given in matrix A as
\[A = \begin{bmatrix}140 \\ 200 \\ 150\end{bmatrix}\begin{array}Telephone \\ House calls \\ Letters\end{array}\]
The number of contacts of each type made in two cities X and Y is given in the matrix B as
\[\begin{array}Telephone & House calls & Letters\end{array}\]
\[B = \begin{bmatrix}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{bmatrix}\begin{array} \\City X \\ City Y\end{array}\]
Find the total amount spent by the party in the two cities.
What should one consider before casting his/her vote − party's promotional activity of their social activities?
If `A= [[3],[5],[2]]` And B=[1 0 4] , Verify that `(AB)^T=B^TA^T`
If `A=[[-2],[4],[5]]` , B = [1 3 −6], verify that (AB)T = BT AT
Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.
If A = [aij] is a square matrix such that aij = i2 − j2, then write whether A is symmetric or skew-symmetric.
Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.
If AB = A and BA = B, where A and B are square matrices, then
If S = [Sij] is a scalar matrix such that sij = k and A is a square matrix of the same order, then AS = SA = ?
If A = [aij] is a scalar matrix of order n × n such that aii = k, for all i, then trace of A is equal to
If \[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\]
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.
If matrix AB = O, then A = O or B = O or both A and B are null matrices.
If A `= [(1,3),(3,4)]` and A2 − kA − 5I = 0, then the value of k is ______.