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29.
(a) Make up a consistent linear system of five equations in five unknowns that has a lower
triangular coefficient matrix with no zeros on or below the main diagonal.
(b) Devise an efficient procedure for solving your system by hand.
(c) Invent an appropriate name for your procedure.
Indicate whether the statement is always true or sometimes false. Justify each answer.
30.
(a) If is singular, then so is A.
(b) If is symmetric, then so are A and B.
(c) If A is an matrix and has only the trivial solution, then so does .
(d) If is symmetric, then so is A.
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