Advertisements
Advertisements
प्रश्न
The matrix P = `[(0, 0, 4),(0, 4, 0),(4, 0, 0)]`is a ______.
पर्याय
Square matrix
Diagonal matrix
Unit matrix
None
उत्तर
The matrix P = `[(0, 0, 4),(0, 4, 0),(4, 0, 0)]`is a square matrix.
Explanation:
We know that, in a square matrix number of rows are equal to the number of columns.
So the matrix P = `[(0, 0, 4),(0, 4, 0),(4, 0, 0)]`is a square matrix
APPEARS IN
संबंधित प्रश्न
Compute the indicated product.
`[(1),(2),(3)] [2,3,4]`
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]])`
For the following matrices verify the associativity of matrix multiplication i.e. (AB) C = A(BC):
`A=[[4 2 3],[1 1 2],[3 0 1]]`=`B=[[1 -1 1],[0 1 2],[2 -1 1]]` and `C= [[1 2 -1],[3 0 1],[0 0 1]]`
For the following matrices verify the distributivity of matrix multiplication over matrix addition i.e. A (B + C) = AB + AC:
`A=[[2 -1],[1 1],[-1 2]]` `B=[[0 1],[1 1]]` C=`[[1 -1],[0 1]]`
If\[A = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix}\] f (x) = x2 − 2x − 3, show that f (A) = 0
Solve the matrix equations:
[2x 3] `[[1 2],[-3 0]] , [[x],[8]]=0`
If `A= [[1,2,0],[3,-4,5],[0,-1,3]]` compute A2 − 4A + 3I3.
If f (x) = x3 + 4x2 − x, find f (A), where\[A = \begin{bmatrix}0 & 1 & 2 \\ 2 & - 3 & 0 \\ 1 & - 1 & 0\end{bmatrix}\]
Find the matrix A such that `=[[1,2,3],[4,5,6]]=[[-7,-8,-9],[2,4,6],[11,10,9]]`
`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 `A=[[1,1],[0,1]] ,` Prove that `A=[[1,n],[0,1]]` for all positive integers n.
Give examples of matrices
A, B and C such that AB = AC but B ≠ C, A ≠ 0.
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?
The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves ₹ 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?
Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.
If \[A = \begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\] satisfies A4 = λA, then write the value of λ.
If \[A = \begin{bmatrix}- 3 & 0 \\ 0 & - 3\end{bmatrix}\] , find A4.
If A = [aij] is a 2 × 2 matrix such that aij = i + 2j, write A.
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=[[i,0],[0,i ]]` , n ∈ N, then A4n equals
If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
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
Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.
If A = `[(3, -5),(-4, 2)]`, then find A2 – 5A – 14I. Hence, obtain A3.
If A, B and C are square matrices of same order, then AB = AC always implies that B = C
If A `= [(1,3),(3,4)]` and A2 − kA − 5I = 0, then the value of k is ______.
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:
- What is the total amount of money (in Rs.) collected by schools CVC and KVS?
