10 0 T F i Let E-0 3 0 Then E is an elementary matrix with respect to the scalin

Question

10 0 T F i Let E-0 3 0 Then E is an elementary matrix with respect to the scaling operation: 0 1 0 0 11 T F j. Let E- 01Then Es is an elementary matrix with respect to the interchange 1 0 0 operation: ki R3 T F k. If an n × n matrix A is invertible, the columns of A span R". T F I. If an n × n matrix A is invertible, then A is row equivalent to identity T F m. If T : R3 R3 is a linear transformation, then the standard matrix A for T is A- T T T T n. If Ax = 0 only has trivial solution, then the columns of A are linearly independent. o. Let A. B be any two n × n matrics, the product AB might not equal the product BA. p. If an n × n matrix A is invertible, the columns of A are linearly independent. q. If the columns of an m × n matrix A span R". then A has a pivot position in every row F F F F

Explanation / Answer

i.True. E2 can be obtained from I3 by a single row operation, i.e. multiplying the 2nd row of I3 by 3.

j.True. E3 can be obtained from I3 by a single row operation, i.e. interchangeof the 1st and the 3rd rows.

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