Find three 2 times 2 idempotent matrices. (Recall that a square matrix A is idempotent when A^2 = A)

Kyran Hudson 2021-03-12 Answered
Find three 2×2 idempotent matrices. (Recall that a square matrix A is idempotent when A2=A)
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smallq9
Answered 2021-03-13 Author has 106 answers
Step 1
Given data:
The order of the given matrix is: m×n=2×2. The expression for the idempotent matrix is,
x2=x
The expression of the identity matrix of 2×2 is, A=[1001]
The expression for the square of the given matrix is,
A2=[1001][1001]
=[1001]
Substitute the given matrix in the above expression.
A2=A
Step 2
Assume the given matrix of order 2×2. is, B=[0001]
The expression for the square of the given matrix is, B2=[0001][0001]
=[0001]
Substitute the value in the expression.
B2=B
Step 3
Assume the given matrix of order 2×2 is, C=[1100]
The expression for the square of the given matrix is, C2=[1100][1100]
=[1100]
Substitute the value in the expression.
C2=C
[1001],[0001], and [1100]
Thus, three idempotent matrices are
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Jeffrey Jordon
Answered 2022-01-24 Author has 2262 answers

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