A is a 5x5 matrix. We know that there is a non-zero 5x1 vector B such that AB =

Amari Flowers

Amari Flowers

Answered question

2021-08-15

A is a 5x5 matrix. We know that there is a non-zero 5x1 vector B such that AB = 6B. Prove that A - 6I is not invertible

Answer & Explanation

Mayme

Mayme

Skilled2021-08-16Added 103 answers

It is given that A is a 5×5 matrix and there is a non-zero 5×1 vector B such that AB=6B that is (A−6I)B=0.
We have to prove that A−6I is not invertible. If possible let A−6I is invertible.
Then (A6I)1 exist.
Now multiplying both side of (A6I)B=0by(A6I)1wet(A6I)1(A6I)B=(A6I)10B=0
which contradicts that B is a non zero 5×1 matrix.
Thus A−6I is not invertible.

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