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Question

asked 2021-09-13

Show that if \(\displaystyle{A}^{{{2}}}\) is the zero matrix, then the only eigenvalue of A is 0.

asked 2021-09-16

Show that:

a) \(Null(B)\) is a subspace of \(Null(C)\).

b) \(Null(C)^{\bot}\) is a subspace of \(Null(B)^{\bot}\) and, consequently, \(\displaystyle{C}{o}{l}{\left({C}{T}\right)}\) is a subspace of \(\displaystyle{C}{o}{l}{\left({B}{T}\right)}\).

asked 2021-09-20

Consider the \(\displaystyle{3}\times{3}\) matrices with real entrices. Show that the matrix forms a vector space over R with respect to matrix addition and matrix multiplication by scalars?

asked 2021-09-22

\(\begin{bmatrix}1&0&0&0&|&1 \\0&1&0&0&|&2 \\0&0&1&2&|&3 \end{bmatrix}\)