MATH 551 Midterm: MATH 551 KSU Test 1u01
15 Feb 2019
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Name: de ne t : r2 r3 by t (x) = ax where. Find a basis for the image of t and a basis for the nullspace of t : use the test for independence to determine whether the following vectors are indepen- dent: Suppose that b is a 3 4 matrix with rank 1 and that x1, x2, x3 satisfy bx = 0. Show that w is a subspace and determine its dimension. W: consider the following subset of r3: W = x + z y + 2z. 3x + y + 5z (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12: answer the following questions without using a calculator. Explain. (e) find two di erent bases for the column space of a. Use some theorems from linear algebra to justify your answers. 3 3 8 2 (a) compute the reduced echelon form of a. Explain: answer true or false to each of the following questions.
