English

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

Advertisements
Advertisements

Question

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

Options

  • True

  • False

MCQ
True or False

Solution

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
  Is there an error in this question or solution?
Chapter 3: Matrices - Exercise [Page 63]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 3 Matrices
Exercise | Q 88 | Page 63

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`

Find BA


Compute the indicated product.

`[(1, -2),(2,3)][(1,2,3),(2,3,1)]`


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

`A=[[1       3         0],[1        1          0],[4         1         0]]`And    B=`[[0      1          0],[1        0        0],[0           5          1]]`


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

`A = [[1,3,-1],[2,-1,-1],[3,0,-1]]` And `B= [[-2,3,-1],[-1,2,-1],[-6,9,-4]]`

 


Evaluate the following:

`[[1     -1],[0            2],[2           3]]`  `([[1     0        2],[2        0        1]]-[[0             1                 2],[1           0                    2]])`


If A = `[[2       -1],[3             2]]`  and B = `[[0         4],[-1          7]]`find 3A2 − 2B + I


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.

 

Let A =`[[-1            1               -1],[3         -3           3],[5           5             5]]`and B =`[[0                4                  3],[1              -3              -3],[-1               4                 4]]`

, compute A2 − B2.

 

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 [1 1 x] `[[1         0            2],[0           2         1],[2            1           0]] [[1],[1],[1]]` = 0, find x.


 If `[[2     3],[5      7]] [[1      -3],[-2       4]]-[[-4      6],[-9        x]]` find x.


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:

[2x 3] `[[1       2],[-3      0]] , [[x],[8]]=0`


`A=[[3,2, 0],[1,4,0],[0,0,5]]` show that A2 − 7A + 10I3 = 0


\[A = \begin{bmatrix}\cos \alpha + \sin \alpha & \sqrt{2}\sin \alpha \\ - \sqrt{2}\sin \alpha & \cos \alpha - \sin \alpha\end{bmatrix}\] ,prove that

\[A^n = \begin{bmatrix}\text{cos n α} + \text{sin n α}  & \sqrt{2}\text{sin n  α} \\ - \sqrt{2}\text{sin n α} & \text{cos n α} - \text{sin  n  α} \end{bmatrix}\] for all n ∈ N.

 


If A and B are square matrices of the same order, explain, why in general

 (A + B) (A − B) ≠ A2 − B2


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.

 

There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question?


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?


A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interes. Using matrix method, find the amount invested by the trust.

 

Let  `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that 

(AB)T = BT AT

 

Express the matrix \[A = \begin{bmatrix}4 & 2 & - 1 \\ 3 & 5 & 7 \\ 1 & - 2 & 1\end{bmatrix}\] as the sum of a symmetric and a skew-symmetric matrix.

If  \[A = \begin{bmatrix}1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} and B = \begin{bmatrix}1 & - 2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\] and AB = I3, then x + y equals 


If  \[A = \begin{bmatrix}\alpha & \beta \\ \gamma & - \alpha\end{bmatrix}\]  is such that A2 = I, then 

 


If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find A matrix Z such that X + Y + Z is a zero matrix


Prove by Mathematical Induction that (A′)n = (An)′, where n ∈ N for any square matrix A.


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 collected by all three schools DPS, CVC, and KVS?

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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×