find the product of AB? A=begin{bmatrix}3 & 1 6 & 0 5&0 end{bmatrix} B=begin{bmatrix}1 & 5 & 3 -1 & 2 & -3 end{bmatrix} a) begin{bmatrix}2 & 17& 6 6 &

Chesley 2020-12-02 Answered
find the product of AB?
A=[316050]
B=[153123]
a) [21766301852515]
b) [166182103025176]
c) [216232305251217]
d) The product is not defined
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Expert Answer

Macsen Nixon
Answered 2020-12-03 Author has 117 answers
Step 1
Given matrices are:
A=[316050]
and
B=[153123]
We have to find the value of product of A and B or AB.
In general if we have two matrices
A=[abcd]
B=[xyzw]
We can multiply two matrices only when number of columns of first matrix is equal to number of rows of second matrix.
If the order of first matrix is m×n then order of second matrix should be n×p.
Here order of first matrix is 2×2 and order of second matrix is 2×2
Therefore,
AB=[abcd][xyzw]
=[ax+bzay+bwcx+dzcy+dw] We do multiply row by column or column by row.
Step 2
Applying above rule in the given matrices, we get
Here, order of first matrix is 3×2 and order of second matrix is 2×3
So, matrices multiplication in this case is possible.
AB=[316050][153123]
=[3115+2936030+01805025+0150]
=[21766301852515]
Hence, first option is correct.
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Jeffrey Jordon
Answered 2022-01-22 Author has 2064 answers

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