हिंदी

A square matrix where every element is unity is called an identity matrix. - Mathematics

Advertisements
Advertisements

प्रश्न

A square matrix where every element is unity is called an identity matrix.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is False.

Explanation:

Since, in identity matrix all the elements of principal diagonal are unity rest are zero.

e.g., A = `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]` = I3

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Matrices - Exercise [पृष्ठ ६३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 3 Matrices
Exercise | Q 88 | पृष्ठ ६३

वीडियो ट्यूटोरियलVIEW ALL [1]

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)]`


Compute the indicated product:

`[(a,b),(-b,a)][(a,-b),(b,a)]`


Show that AB ≠ BA in each of the following cases:

`A= [[5    -1],[6        7]]`And B =`[[2       1],[3         4]]`


Show that AB ≠ BA in each of the following cases

`A=[[-1          1           0],[0          -1           1],[2                  3                4]]`  and  =B `[[1          2            3], [0          1           0],[1        1          0]]`


Compute the products AB and BA whichever exists in each of the following cases:

A = [1 −1 2 3] and B=`[[0],[1],[3],[2]]`

 


Evaluate the following:

`([[1              3],[-1    -4]]+[[3        -2],[-1         1]])[[1         3           5],[2            4               6]]`


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.

 

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. (ABC = 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]]` 


If\[A = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix}\] f (x) = x2 − 2x − 3, show that f (A) = 0


Find the value of x for which the matrix product`[[2       0           7],[0          1            0],[1       -2       1]]` `[[-x         14x          7x],[0         1            0],[x           -4x             -2x]]`equal an identity matrix.


`A=[[1,0,-3],[2,1,3],[0,1,1]]`then verify that A2 + A = A(A + I), where I is the identity matrix.


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.


Give examples of matrices
A and B such that AB ≠ BA


Give examples of matrices

A and B such that AB = O but BA ≠ O.


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 ≠ CA ≠ O.

 

Three shopkeepers AB 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
\[A = \begin{bmatrix}140 \\ 200 \\ 150\end{bmatrix}\begin{array} \text{Telephone}\\{\text{House calls }}\\ \text{Letters}\end{array}\]

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 

 (A + B)T = AT BT


Let `A= [[1,-1,0],[2,1,3],[1,2,1]]` And `B=[[1,2,3],[2,1,3],[0,1,1]]` Find `A^T,B^T` and verify that (2A)T = 2AT.


 For two matrices A and B,   \[A = \begin{bmatrix}2 & 1 & 3 \\ 4 & 1 & 0\end{bmatrix}, B = \begin{bmatrix}1 & - 1 \\ 0 & 2 \\ 5 & 0\end{bmatrix}\](AB)T = BT AT.

 


If \[A = \begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\] satisfies A4 = λA, then write the value of λ.

 

 


If A = [aij] is a square matrix such that aij = i2 − j2, then write whether A is symmetric or skew-symmetric.


If `A=[[i,0],[0,i ]]` , n ∈ N, then A4n equals


If S = [Sij] is a scalar matrix such that sij = k and A is a square matrix of the same order, then AS = SA = ? 


The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is


If \[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\] 


If A = `[(0, 1),(1, 0)]`, then A2 is equal to ______.


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 money (in Rupees) collected by the school DPS?

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×