We are told that a certain matrix can be written as
where is and is . Explain how you know that is not invertible.
Thus, it is proved matrix is not invertible.
Let matrix is which is where is and is .
Let assume that . There are different ways and one way is as the linear transformation is the composition of and gives .
Take dimensions where . Now by the rank-nullity theorem applied to , gives.
Which implies that is never 5, that is needed for to be invertible.
Hence, matrixis not invertible.
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