verify that (AB)^T = B^TA^T If A=begin{bmatrix}2 & 1 6 & 3 -2&4 end{bmatrix} text{ and } B=begin{bmatrix}2 & 4 1 & 6 end{bmatrix}

kuCAu 2020-12-12 Answered
verify that (AB)T=BTAT
If A=[216324] and B=[2416]
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Expert Answer

2k1enyvp
Answered 2020-12-13 Author has 94 answers
Step 1
Given matrices:
A=[216324]
B=[2416]
Now, Transpose of a matrix is given by turning rows into columns:
AT=[216324]T=[262134]
BT=[2416]T=[2146]
Step 2
Product of given matrices:
AB=[216324][2416]
=[22+1124+1662+3164+36(2)2+41(2)4+46]
=[5141542016]
And its transpose is:
(AB)T=[5141542016]T=[5150144216]
Step 3
Product of transpose of given matrices:
BTAT=[2146][262134]
=[22+1126+132(2)+1442+6146+634(2)+64]
=[5150144216]
Therefore,
(AB)T=BTAT=[5150144216]
Hence, verified.
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