मराठी

If a is a Matrix of Order M × N and B is a Matrix Such that Abt and Bta Are Both Defined, Then the Order of Matrix B is Disclaimer: Option (A) and (D) Both Are the Same. - Mathematics

Advertisements
Advertisements

प्रश्न

If A is a matrix of order m × n and B is a matrix such that ABT and BTA are both defined, then the order of matrix B is 

Disclaimer: option (a) and (d) both are the same.

 

पर्याय

  •  m × n

  • n  × n 

  • n × m

  • m  × n

MCQ

उत्तर

Since, ABT and BTA are both defined.

And, order of A is m × n. So, Order of BT must be n × m.

Thus, order of matrix B is m × n.

Hence, the correct option is (d).

 
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Algebra of Matrices - Exercise 5.7 [पृष्ठ ६९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 5 Algebra of Matrices
Exercise 5.7 | Q 38 | पृष्ठ ६९

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Compute the indicated product:

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


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]]`

 


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

 [ab]`[[c],[d]]`+ [a, b, c, d] `[[a],[b],[c],[d]]`


Evaluate the following:

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


Evaluate the following:

`[[],[1  2  3],[]]` `[[1     0      2],[2       0         1],[0          1       2]]` `[[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.

 

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]]` 


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]]`

 


If [1 1 x] `[[1         0            2],[0           2         1],[2            1           0]] [[1],[1],[1]]` = 0, 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:

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


If f (x) = x2 − 2x, find f (A), where A=


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

 

Find a 2 × 2 matrix A such that `A=[[1,-2],[1,4]]=6l_2`


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


 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).`


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

(A + B)2 ≠ A2 + 2AB + B2


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

 (2A)T = 2AT


If `A=[[-2],[4],[5]]` , B = [1 3 −6], verify that (AB)T = BT AT

 

 If \[A = \begin{bmatrix}2 & 4 & - 1 \\ - 1 & 0 & 2\end{bmatrix}, B = \begin{bmatrix}3 & 4 \\ - 1 & 2 \\ 2 & 1\end{bmatrix}\],find `(AB)^T`

 


 If \[A = \begin{bmatrix}\sin \alpha & \cos \alpha \\ - \cos \alpha & \sin \alpha\end{bmatrix}\] , verify that AT A = I2.
 

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

 

 


If I is the identity matrix and A is a square matrix such that A2 = A, then what is the value of (I + A)2 = 3A?


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


If  \[\begin{bmatrix}\cos\frac{2\pi}{7} & - \sin\frac{2\pi}{7} \\ \sin\frac{2\pi}{7} & \cos\frac{2\pi}{7}\end{bmatrix}^k = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\] then the least positive integral value of k is _____________.


Let A = \[\begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{bmatrix}\], then An is equal to

 


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


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


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 matrix  \[A = \begin{bmatrix}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{bmatrix}\] is a


If A is a square matrix such that A2 = I, then (A − I)3 + (A + I)3 − 7A is equal to 


If A and B are square matrices of the same order, then (A + B)(A − B) is equal to 


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


If A = `[(3, 5)]`, B = `[(7, 3)]`, then find a non-zero matrix C such that AC = BC.


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?

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×