ch em ins ing in n. lem the wing n in lem solution of 12. Construct a 2 x 3 matrix A, not in echel solution of Ax = 0 is a plane in R³. 13. Write the reduced echelon form of a 3 x 3 matrix A such that the first two columns of A are pivot columns and 3 []-[8] A 14. Determine the value(s) of a such that linearly independent. 15. In (a) and (b), suppose the vectors are linearly independent. f? Justify your What can you say about the numbers a, ..., answers. [Hint: Use a theorem for (b).] LATE a 000-000 b. a. a A = 1 2 b 3 4 is -[:] [₂] - d 16. Use Theorem 7 in Section 1.7 to explain why the columns of the matrix A are linearly independent. 0 0 0 5 0 0 6 8 0 7 9 10 b d 17. Explain why a set {V1, V2, V3, V4} in R5 must be linearly independent when {V₁, V2, V3} is linearly independent and V4 is not in Span {V₁, V2, V3}. 18. Suppose (V₁, V2} is a linearly independent set in R". Show that (V₁, V₁ + V₂} is also linearly independent.

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