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

Dolly Robinson

Answered question


Solve the equation forX, given that
commutes with both [1000] and [0001]

Answer & Explanation



Skilled2021-01-14Added 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,
Step 2
Now, B=[abcd] commutes with [1000]
So, a=a, b=c=d=0
Also, B=[abcd] commutes with [0001]
So, d=d, a=b=c0
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

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