Solve the equation forX, given that B=begin{bmatrix}a & b c & d end{bmatrix} commutes with both begin{bmatrix}1 & 0 0 & 0 end{bmatrix} and begin{bmatrix}0 & 0 0 & 1 end{bmatrix}

Dolly Robinson 2021-01-13 Answered
Solve the equation forX, given that
B=[abcd]
commutes with both [1000] and [0001]
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Expert Answer

liannemdh
Answered 2021-01-14 Author has 106 answers
Step 1
To show that the given matrix B commutes with the other two matrices,
B=[abcd] commutes with [1000] and [0001]
To find the conditions on a, b, c, d.
For commutativity,
AB=BA
Step 2
Now, B=[abcd] commutes with [1000]
[abcd][1000]=[1000][abcd]
[a0c0]=[ab00]
So, a=a, b=c=d=0
Also, B=[abcd] commutes with [0001]
[abcd][0001]=[0001][abcd]
[0b0d]=[00cd]
So, d=d, a=b=c0
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Jeffrey Jordon
Answered 2022-01-30 Author has 2064 answers

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