Compute the product AB by the definition of the product of matrices, where Ab1 and Ab2 are computed separately, and by the row-comumn rule for computing AB. A=[−23356−2], B=[5−1−14] Set up the product Ab1, where b1 is the first column of B. Ab1=?? where b1 is the first column of B. Calculate Ab1 where b1 is the first column of of B. Ab1=? Set up the product Ab2 where b2 is the second column of B Ab2=? Calculate Ab2 where b2 is the second column of B. Ab2=? Determine the numerical expression for the first entry in the first column of AB using the row-column rule.

Question

Compute the product AB by the definition of the product of matrices, where Ab1 and Ab2 are computed separately, and by the row-comumn rule for computing AB. A=[−23356−2], B=[5−1−14] Set up the product Ab1, where b1 is the first column of B. Ab1=?? where b1 is the first column of B. Calculate Ab1 where b1 is the first column of of B. Ab1=? Set up the product Ab2 where b2 is the second column of B ​Ab2=? Calculate Ab2 where b2 is the second column of B. Ab2=? Determine the numerical expression for the first entry in the first column of AB using the​ row-column rule.

porschomcl · Accepted Answer

We will use the product method of matrix to find solution to the problem.  Set up the product Ab1, where b, is the first column of B.  Ab1=−2,5+3,−1  =−10+(−3)  =−10−3  =−13  Calculate Ab1 where b1 is the first column of B  Ab1=−13  Set up the product Ab2, where b1 is the second column of B.  Ab2=−2,−1+3,4  ⇒2+12  ⇒14  Calculate Ab2, where b2 is the second column of B.  Ab2=14  For the first entry,  ((−2)(5)+(3)(−1)) is correct  Product AB=  [−1314101732−14]

Archie Jones · Accepted Answer

The calculation of Ab1 is as follows:  Ab1=  [−22344−3][4−1]  =[−2(4)+2(−1)3(4)+4(−1)4(4)+(−3)(−1)]  =[−8−212−416+3]  [−10819]  Therefore, Ab1= [−10819]  The product Ab2= [−22344−3][−12]  The calculation of Ab1 is as follows:  Ab2=ZSK[−22344−3][−12]  =[−2(−1)+2(2)3(−1)+4(2)4(−1)+(−3)(2)]  =[2+4−3+8−4−6]  =[65−10]  Therefore, Ab2=ZSK[65−10]  Write the matrix AB as  [AB= [−2(4)+2(−1)−2(−1)+2(2)3(4)+4(−1)3(−1)+4(2)4(4)+(−3)(−1)4(−1)+(−3)(2)]]  Thus, the first entry in the first column of the matrix AB is −2(4)+2(−1).  Hence, the correct option is (C).  The final product of the matrices A and B is AB= [−1068519−10]