मराठी

Let A=[2432],B=[13-25],C=[-2534] Find BA - Mathematics

Advertisements
Advertisements

प्रश्न

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

Find BA

बेरीज

उत्तर

Matrix B has 2 columns. This number is equal to the number of rows in matrix A. Therefore, BA is defined as:

`BA = [(1,3),(-2,5)][(2,4),(3,2)]`

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

=`[(2+9, 4+6), (-4+15, -8+10)]`

=`[(11,10),(11,2)]`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Matrices - Exercise 3.2 [पृष्ठ ८०]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 3 Matrices
Exercise 3.2 | Q 1.5 | पृष्ठ ८०

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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

Find AB


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 product:

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


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]]`

 


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

 

If A = `[[ cos 2θ     sin 2θ],[ -sin 2θ    cos 2θ]]`, find A2.


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.

 

If A= `[[1        0           -2],[3        -1           0],[-2              1               1]]` B=,`[[0         5           -4],[-2          1             3],[-1          0              2]] and  C=[[1               5              2],[-1           1              0],[0          -1             1]]` verify that A (B − C) = AB − AC.


If [1 −1 x] `[[0       1           -1],[2           1             3],[1          1             1]]   [[0],[1],[1]]=`= 0, find x.


\[A = \begin{bmatrix}3 & - 2 \\ 4 & - 2\end{bmatrix} and \text{ I }= \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\],  then prove that A2 − A + 2I = O.


If A=then find λ, μ so that A2 = λA + μI

 

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.


Solve the matrix equations:

`[[],[x-5-1],[]][[1,0,2],[0,2,1],[2,0,3]] [[x],[4],[1]]=0`


Solve the matrix equations:

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


If , then show that A is a root of the polynomial f (x) = x3 − 6x2 + 7x + 2.

 

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


If `A=[[0,-x],[x,0]],[[0,1],[1,0]]` and `x^2=-1,` then  show that `(A+B)^2=A^2+B^2`


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

(− B)2 ≠ A2 − 2AB + B2


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.

 

The cooperative stores of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs. 8.30, Rs. 3.45 and Rs. 4.50 each respectively. Find the total amount the store will receive from selling all the items.

 

In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as

      Cost per contact

`A=[[40],[100],[50]]` `[["Teliphone"] ,["House call "],[" letter"]]`

The number of contacts of each type made in two cities X and Y is given in matrix B as

       Telephone   House call    Letter

`B= [[    1000, 500,      5000],[3000,1000,     10000                ]]` 

Find the total amount spent by the group in the two cities X and Y.

 

A trust fund has Rs 30000 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 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of(ii) Rs 2000


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.


If  \[A = \begin{bmatrix}\cos x & - \sin x \\ \sin x & \cos x\end{bmatrix}\]  , find AAT

 

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

 


If  \[\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\begin{bmatrix}3 & 1 \\ 2 & 5\end{bmatrix} = \begin{bmatrix}7 & 11 \\ k & 23\end{bmatrix}\] ,then write the value of k.


If A is 2 × 3 matrix and B is a matrix such that AT B and BAT both are defined, then what is the order of B ?


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 number of possible matrices of order 3 × 3 with each entry 2 or 0 is 


If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find X + Y


If A and B are square matrices of the same order, then [k (A – B)]′ = ______.


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?

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. 1,800.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×