English

Compute the indicated product. [3-13-102][2-31031] - Mathematics

Advertisements
Advertisements

Question

Compute the indicated product.

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

Sum

Solution

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

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

`= [(6-1+9, -9-0+3), (-2+0+6, 3+0+2)]`

`= [(14, -6),(4,5)]`

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Matrices - Exercise 3.2 [Page 80]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 3 Matrices
Exercise 3.2 | Q 3.6 | Page 80

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 products

`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`


A trust fund has Rs. 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of Rs 2,000.


Compute the indicated products:

`[[a    b],[-b      a]][[a     -b],[b         a]]`


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=[[3     2],[-1     0],[-1      1]]` and `B= [[4         5        6],[0           1             2]]`


Evaluate the following:

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


If A =  `[[4       2],[-1        1]]` 

, prove that (A − 2I) (A − 3I) = O

 

If A = `[[ab,b^2],[-a^2,-ab]]` , show that A2 = O

 

If A =

\[\begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\]and B =

\[\begin{bmatrix}- 1 & 3 & 5 \\ 1 & - 3 & - 5 \\ - 1 & 3 & 5\end{bmatrix}\] , show that AB = BA = O3×3.


Compute the elements a43 and a22 of the matrix:`A=[[0     1        0],[2      0        2],[0       3        2],[4        0       4]]` `[[2       -1],[-3           2],[4              3]]  [[0            1           -1                    2                     -2],[3       -3             4          -4                  0]]`

 


\[A = \begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\]   , Show that A2 = A.


If [x 4 1] `[[2       1          2],[1         0          2],[0       2 -4]]`  `[[x],[4],[-1]]` = 0, find x.

 


If


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


If A=, find k such that A2 = kA − 2I2

 

Find the matrix A such that    [2  1  3 ] `[[-1,0,-1],[-1,1,0],[0,1,1]] [[1],[0],[-1]]=A`


 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).`


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

 


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


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

(− B)2 ≠ A2 − 2AB + B2


To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:

(i) ₹50       (ii) ₹20       (iii) ₹40

The number of attempts made in three villages XY and Z are given below:

          (i)               (ii)              (iii)
X      400              300             100
Y      300              250               75
Z      500              400             150

Find the total cost incurred by the organisation for three villages separately, using matrices.

 

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?


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   (A + B)T = AT + BT


If the matrix \[A = \begin{bmatrix}5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7\end{bmatrix}\]  is a symmetric matrix, find xyz and t.
 

 


 If \[A = \begin{bmatrix}4 & 3 \\ 1 & 2\end{bmatrix} and B = \binom{ - 4}{ 3}\] 

write AB.

 

 If \[A = \begin{bmatrix}- 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\] , find A2.
 

 


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 are square matrices of order 3, A is non-singular and AB = O, then B is a 


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


If A = `[(2, -1, 3),(-4, 5, 1)]` and B = `[(2, 3),(4, -2),(1, 5)]`, then ______.


Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.


If matrix A = [aij]2×2, where aij `{:(= 1  "if i" ≠ "j"),(= 0  "if i" = "j"):}` then A2 is equal to ______.


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:

  • What is the total amount of money (in Rs.) collected by schools CVC and KVS?

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 = `[(-3, -2, -4),(2, 1, 2),(2, 1, 3)]`, B = `[(1, 2, 0),(-2, -1, -2),(0, -1, 1)]` then find AB and use it to solve the following system of equations:

x – 2y = 3

2x – y – z = 2

–2y + z = 3


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×