137 EXAMPLE 2 aurez v 12-17 If A = ...
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137 EXAMPLE 2 aurez v 12-17 If A = 3 4 and B = 1 5 m -[21]. Find AB. Dos BA estar find AB. Does BA exist?

11th - 12th Class
Maths
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Here ( A ) is a ( 3 times 2 ) matrix and ( B ) is a ( 2 times 2 ) matrix. Clearly, the number of columns in ( A ) equals the number of rows in ( B ) ( A B ) exists and it is a ( 3 times 2 ) matrix. [ begin{aligned} text { Now, } A B &=left[begin{array}{rr} 2 & -1 3 & 4 1 & 5 end{array}right]left[begin{array}{rr} -1 & 3 2 & 1 end{array}right] &=left[begin{array}{rr} 2 cdot(-1)+(-1) cdot 2 & 2 cdot 3+(-1) cdot 1 3 cdot(-1)+4 cdot 2 & 3 cdot 3+4 cdot 1 1 cdot(-1)+5 cdot 2 & 1 cdot 3+5 cdot 1 end{array}right] &=left[begin{array}{rr} -4 & 5 5 & 13 9 & 8 end{array}right] end{aligned} ] Further, ( B ) is a ( 2 times 2 ) matrix and ( A ) is a ( 3 times 2 ) matrix. So, the number of columns in ( B ) is not equal to the number of rows in ( A ). So, ( B A ) does not exist.
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