MATH 1553 Quiz: MATH 1553 GT Quiz 4 1 7 to 1 9 Solutionsm1553
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Math 1553 quiz 4: 1. 7, 1. 8, 1. 9 (10 points, 10 minutes) 1. (3 points) in each case, determine whether the set of vectors is linearly dependent or linearly independent. You do not need to justify your answer. 3 linearly dependent linearly independent linearly dependent linearly independent linearly dependent linearly independent (a) forming a matrix a with the vectors as columns gives 3 pivot columns (no row- reduction required). R3: true or false (no justi cation required): it is possible that t is onto. It is impossible for any linear transformation t : r3. It would require a to have a pivot in every row, which is impossible since a 4 3 matrix has at most 3 pivots. R2 be the transformation which re ects about the line y = x, (5 pts) let t : r2 then rotates counterclockwise by 45 . Find the matrix a so that t (x) = ax for all x in r2.
