हिंदी

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.

 

विकल्प

  •  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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Algebra of Matrices - Exercise 5.7 [पृष्ठ ६९]

APPEARS IN

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

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Compute the indicated product:

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


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


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]]`


If A =  `[[1    1],[0    1]]`  show that A2 = `[[1       2],[0          1]]` and A3 = `[[1        3],[0       1]]`


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.


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


\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix}\]show that A2 − 5A + 7I = O use this to find A4.


Find the matrix A such that `=[[1,2,3],[4,5,6]]=[[-7,-8,-9],[2,4,6],[11,10,9]]`


If\[A = \begin{bmatrix}a & b \\ 0 & 1\end{bmatrix}\], prove that\[A^n = \begin{bmatrix}a^n & b( a^n - 1)/a - 1 \\ 0 & 1\end{bmatrix}\] for every positive integer n .


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.

 

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

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 

 (2A)T = 2AT


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

 (A + B)T = AT BT


If `A= [[3],[5],[2]]` And B=[1  0   4] , Verify that `(AB)^T=B^TA^T` 


For the matrices A and B, verify that (AB)T = BT AT, where
\[A = \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}, B = \begin{bmatrix}1 & 4 \\ 2 & 5\end{bmatrix}\]

If A is an m × n matrix and B is n × p matrix does AB exist? If yes, write its order.

 

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

 

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 ?


Write a 2 × 2 matrix which is both symmetric and skew-symmetric.


If AB = A and BA = B, where A and B are square matrices,  then


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


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

 


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


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


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


The matrix P = `[(0, 0, 4),(0, 4, 0),(4, 0, 0)]`is a ______.


If A and B are two square matrices of the same order, then AB = BA.


If A `= [(1,3),(3,4)]` and A2 − kA − 5I = 0, then the value of k is ______.


If A `= [(1,-2,1),(2,1,3)]` and B `= [(2,1),(3,2),(1,1)],` then (AB)T is equal


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?

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:

  • If the number of handmade fans and plates are interchanged for all the schools, then what is the total money collected by all schools?

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×