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

Lewis Harvey

Answered question

2021-02-09

verify that (AB)C = A(BC)
If A=[2413],B=[2104],C=[3121]

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-02-10Added 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]
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-22Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?