Prove Theorem 4.3a,c-f.
Prove Theorem 4.22, parts a, b, d, e.
Prove Theorems 5.1 and 5.2 .
Prove Theorem 3.4(d).
Prove Theorems 3.6 and 3.9(a-d).
Prove Theorem 3.19.
Explain why b is in the span of the columns of A iff the system [A | b] has a solution.
Explain why the columns of A are linearly dependent iff the system [A | 0] has a nontrivial solution.
Explain why if A is invertible then Ax=b has a unique solution.
Explain why if A is invertible then Ax=0 has only the trivial solution.
Explain why if A is invertible and has n columns then col(A) is R^n.
Explain why a square matrix is invertible iff its columns are linearly independent.
Suppose matrix B is obtained from matrix A by one elementary row operation. Prove that columns k_1, k_2, ..., k_r of A are linearly dependent iff columns k_1, k_2, ..., k_r of B are linearly dependent.
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