Question: Construct a (simple ?) (2 2) matrix A such that for any vector b R2 system Ax = b has exactly one solution, and Ax

Construct a (simple ?) (2 2) matrix A such that for any vector b R2 system Ax = b has exactly one solution, and Ax = 0 has only the trivial solutiion. Justify your claims about the number of solutions.

Take the matrix A from the problem 1 above, and consider the operator T (x) = Ax. Explain why this operator is "onto".

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