हिंदी

If matrix AB = O, then A = O or B = O or both A and B are null matrices. - Mathematics

Advertisements
Advertisements

प्रश्न

If matrix AB = O, then A = O or B = O or both A and B are null matrices.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is False.

Explanation:

Since for any two non-zero matrices A and B, we may get AB = 0.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Matrices - Exercise [पृष्ठ ६३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 3 Matrices
Exercise | Q 91 | पृष्ठ ६३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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

Find AB


Compute the indicated product.

`[(1),(2),(3)] [2,3,4]`


Compute the indicated product:

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


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]]`


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


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 `A= [[1,2,0],[3,-4,5],[0,-1,3]]` compute A2 − 4A + 3I3.


`A=[[1,0,-3],[2,1,3],[0,1,1]]`then verify that A2 + A = A(A + I), where I is the identity matrix.


Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?

 

Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2 B2? Give reasons.

 

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.

 

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?


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


 For two matrices A and B,   \[A = \begin{bmatrix}2 & 1 & 3 \\ 4 & 1 & 0\end{bmatrix}, B = \begin{bmatrix}1 & - 1 \\ 0 & 2 \\ 5 & 0\end{bmatrix}\](AB)T = BT AT.

 


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

 

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

write AB.

 

If  \[A = \begin{bmatrix}1 \\ 2 \\ 3\end{bmatrix}\] write AAT.

 


If \[A = \begin{bmatrix}- 3 & 0 \\ 0 & - 3\end{bmatrix}\] , find A4.


If A is a matrix of order 3 × 4 and B is a matrix of order 4 × 3, find the order of the matrix of AB


For a 2 × 2 matrix A = [aij] whose elements are given by 

\[a_{ij} = \frac{i}{j}\] , write the value of a12.
 

If A is a square matrix such that A2 = A, then write the value of 7A − (I + A)3, where I is the identity matrix.


Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.


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


Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A(BC) = (AB)C


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?

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×