Advertisements
Advertisements
प्रश्न
If [1 1 x] `[[1 0 2],[0 2 1],[2 1 0]] [[1],[1],[1]]` = 0, find x.
उत्तर
Given : [1 1 x] `[[1,0,2],[0,2,1],[2,1 ,0]] [[1],[1],[1]]=0`
⇒[1+0+2x 0+2+x 2+1+0] `[[1],[1],[1]]=0`
⇒[1+2x 2+x 3] `[[1],[1],[1]]=0`
⇒[1+2x+2+x+3]=0
⇒6+3x=0
⇒3x=−6
⇒x=`(-6)/3`
∴ x=-2
APPEARS IN
संबंधित प्रश्न
Compute the indicated product.
`[(1, -2),(2,3)][(1,2,3),(2,3,1)]`
Compute the indicated product:
`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`
If A = `[[2 -1],[3 2]]` and B = `[[0 4],[-1 7]]`find 3A2 − 2B + I
If A = `[[ab,b^2],[-a^2,-ab]]` , show that A2 = O
If A = `[[0,c,-b],[-c,0,a],[b,-a,0]]`and B =`[[a^2 ,ab,ac],[ab,b^2,bc],[ac,bc,c^2]]`, show that AB = BA = O3×3.
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]]`
\[A = \begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\] , Show that A2 = A.
If [x 4 1] `[[2 1 2],[1 0 2],[0 2 -4]]` `[[x],[4],[-1]]` = 0, find x.
If `[[2 3],[5 7]] [[1 -3],[-2 4]]-[[-4 6],[-9 x]]` find x.
Solve the matrix equations:
`[x1][[1,0],[-2,-3]][[x],[5]]=0`
Solve the matrix equations:
`[1 2 1] [[1,2,0],[2,0,1],[1,0 ,2]][[0],[2],[x]]=0`
`A=[[3,2, 0],[1,4,0],[0,0,5]]` show that A2 − 7A + 10I3 = 0
Find the matrix A such that `[[2,-1],[1,0],[-3,-4]]A` `=[[-1,-8,-10],[1,-2,-5],[9,22,15]]`
`A=[[1,0,-3],[2,1,3],[0,1,1]]`then verify that A2 + A = A(A + I), where I is the identity matrix.
If `P(x)=[[cos x,sin x],[-sin x,cos x]],` then show that `P(x),P(y)=P(x+y)=P(y)P(x).`
If `P=[[x,0,0],[0,y,0],[0,0,z]]` and `Q=[[a,0,0],[0,b,0],[0,0,c]]` prove that `PQ=[[xa,0,0],[0,yb,0],[0,0,zc]]=QP`
If `A=[[1,1],[0,1]] ,` Prove that `A=[[1,n],[0,1]]` for all positive integers n.
Let `A= [[1,1,1],[0,1,1],[0,0,1]]` Use the principle of mathematical introduction to show that `A^n [[1,n,n(n+1)//2],[0,1,1],[0,0,1]]` for every position integer n.
If A and B are square matrices of the same order such that AB = BA, then show that (A + B)2 = A2 + 2AB + B2.
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?
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that
(2A)T = 2AT
If `A=[[-2],[4],[5]]` , B = [1 3 −6], verify that (AB)T = BT AT
If A is a matrix of order 3 × 4 and B is a matrix of order 4 × 3, find the order of the matrix of AB.
For a 2 × 2 matrix A = [aij] whose elements are given by
Write a 2 × 2 matrix which is both symmetric and skew-symmetric.
Construct a 2 × 2 matrix A = [aij] whose elements aij are given by \[a_{ij} = \begin{cases}\frac{\left| - 3i + j \right|}{2} & , if i \neq j \\ \left( i + j \right)^2 & , if i = j\end{cases}\]
If A and B are two matrices such n that AB = B and BA = A , `A^2 + B^2` is equal to
If A is a square matrix such that A2 = A, then (I + A)3 − 7A is equal to
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
(a) nk (b) n + k (c) \[\frac{n}{k}\] (d) none of these
The matrix \[A = \begin{bmatrix}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{bmatrix}\] is a
If A and B are square matrices of the same order, then (A + B)(A − B) is equal to
If A = `[(3, 5)]`, B = `[(7, 3)]`, then find a non-zero matrix C such that AC = BC.
A matrix which is not a square matrix is called a ______ matrix.
A square matrix where every element is unity is called an identity matrix.
Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as
School/Article | DPS | CVC | KVS |
Handmade/fans | 40 | 25 | 35 |
Mats | 50 | 40 | 50 |
Plates | 20 | 30 | 40 |
Based on the information given above, answer the following questions:
- How many articles (in total) are sold by three schools?
If A = `[(1, 1, 1),(0, 1, 1),(0, 0, 1)]` and M = A + A2 + A3 + .... + A20, then the sum of all the elements of the matrix M is equal to ______.