Find the order of B matrix if A is a $3 \times 4$ matrix and B is a matrix such that A’B and BA’ are both defined.:
$(a){\text{ 3}} \times {\text{4}}$
$(b){\text{ 3}} \times 3$
$(c){\text{ 4}} \times {\text{4}}$
$(d){\text{ 4}} \times 3$
Last updated date: 30th Mar 2023
•
Total views: 306.6k
•
Views today: 5.83k
Answer
306.6k+ views
Hint: In the above given question, we are asked to find out the order of the matrix for which various conditions are already provided. By using these conditions one by one, first of all find out the number of rows in the matrix and then using the other conditions, find out the number of columns in the given matrix.
Complete step-by-step answer:
We are given in the question that, A is a $3 \times 4$ matrix, therefore we know that,
Order of A’ will be ${\text{4}} \times 3$.
Since, it is given that A’B exists and we already know that A’ is a ${\text{4}} \times 3$ matrix.
Hence, we can conclude that B must have 3 rows.
Also, it is given in the question that, BA’ exists, therefore we come to know that,
B must have 4 columns.
Now, we know that B has 3 rows and 4 columns, so we can say that B is a $3 \times 4$ matrix.
Hence, the required solution is the option $(a){\text{ 3}} \times {\text{4}}$.
Note: When we face such types of problems, the key concept is to have a good knowledge of the matrices and its properties particularly regarding order of the matrix. By using these properties and the conditions already provided to us in the question, we can obtain the required solution.
Complete step-by-step answer:
We are given in the question that, A is a $3 \times 4$ matrix, therefore we know that,
Order of A’ will be ${\text{4}} \times 3$.
Since, it is given that A’B exists and we already know that A’ is a ${\text{4}} \times 3$ matrix.
Hence, we can conclude that B must have 3 rows.
Also, it is given in the question that, BA’ exists, therefore we come to know that,
B must have 4 columns.
Now, we know that B has 3 rows and 4 columns, so we can say that B is a $3 \times 4$ matrix.
Hence, the required solution is the option $(a){\text{ 3}} \times {\text{4}}$.
Note: When we face such types of problems, the key concept is to have a good knowledge of the matrices and its properties particularly regarding order of the matrix. By using these properties and the conditions already provided to us in the question, we can obtain the required solution.
Recently Updated Pages
If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
