verify that (AB)C = A(BC) If A=begin{bmatrix}2 & 4 1 & 3 end{bmatrix}, B=begin{bmatrix}-2 & 1 0 & 4 end{bmatrix},C=begin{bmatrix}3 & 1 2 & 1 end{bmatrix}

Lewis Harvey 2021-02-09 Answered
verify that (AB)C = A(BC)
If A=[2413],B=[2104],C=[3121]
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Expert Answer

Bentley Leach
Answered 2021-02-10 Author has 109 answers
Step 1
Given matrices:
A=[2413],B=[2104],C=[3121] Step 2 Calculate (AB)C:
AB=[2413][2104]
=[2×(2)+4×02×1+4×41×(2)+3×01×1+3×4]
=[418213]
AB(C)=[418213][3121]
=[(4)×3+18×2(4)×1+18×1(2)×3+13×2(2)×1+13×1]
=[24142011]
Step 3
Calculate A(BC)
BC=[2104][3121]
=[2×3+1×22×1+1×10×3+4×20×1+4×1]
=[4184]
A(BC)=[2413][4184]
=[2×(4)+4×82×(1)+4×41×(4)+3×81×(1)+3×4]
=[24142011]
Step 4
Thus,
A(BC)=(AB)C=[24142011]
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