Find AB, if A = $open square brackets table row 6 9 row 2 3 end table close square brackets space and space space straight B space equals space open square brackets table row 2 6 0 row 7 9 8 end table close square brackets$

Solution

Here $A equals open square brackets table row bold 6 bold 9 row bold 2 bold 3 end table close square brackets bold space bold B bold space bold equals bold space open square brackets table row bold 2 bold 6 bold 0 row bold 7 bold 9 bold 8 end table close square brackets$

The matrix A is of type 2 x 2 and B is of type 2 x 3.
Number of columns of A = number of rows of B = 2. So AB is defined
$AB equals open square brackets table row 6 9 row 2 3 end table close square brackets open square brackets table row 2 6 0 row 7 9 8 end table close square brackets space space space space equals space open square brackets table row cell left parenthesis 6 right parenthesis left parenthesis 2 right parenthesis left parenthesis 9 right parenthesis left parenthesis 7 right parenthesis end cell cell left parenthesis 6 right parenthesis left parenthesis 6 right parenthesis plus left parenthesis 9 right parenthesis left parenthesis 9 right parenthesis end cell cell left parenthesis 6 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis 9 right parenthesis left parenthesis 8 right parenthesis end cell row cell left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 7 right parenthesis end cell cell left parenthesis 2 right parenthesis left parenthesis 6 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 9 right parenthesis end cell cell left parenthesis 2 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 8 right parenthesis end cell end table close square brackets space space space space equals space open square brackets table row cell 12 plus 63 end cell cell 36 plus 81 end cell cell 0 plus 72 end cell row cell 4 plus 21 end cell cell 12 plus 27 end cell cell 0 plus 24 end cell end table close square brackets therefore space space AB equals open square brackets table row 75 117 72 row 25 39 24 end table close square brackets$

Note 1. Here AB is defined. But BA is not defined as number of columns of B is not equal to number of rows of A.
Note 2. If A and B are square matrices of the same order, then AB and BA are both defined.

For Daily Free Study Material Join wiredfaculty

Matrices

Find AB, if A = $open square brackets table row 6 9 row 2 3 end table close square brackets space and space space straight B space equals space open square brackets table row 2 6 0 row 7 9 8 end table close square brackets$

Some More Questions From Matrices Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction