1 1 Answer True or False for each of the following For all q

1. 1. Answer True or False for each of the following: For all questions below, assume that A and B are n x n matrices. (22 Pts) (a) If tv1, t 2) is early independent and va g Spanfer, 2) then (Vi v2.val is also linearly independent. (b) If He1. is nearly independent then (v1, v2, us, is also linearly independent. (c) If (er, v2, us) is arly dependent then is also linearly depend lent (d) T R3 R can not be a one-to-one linear transformation. (e) T R R can not be an onto linear transformation If A is an n x n matrix and AF has infinitely many solutions for a specific 61 then the columns of A are linearly dependent. (g) If T R\" R\" is a linear transformation such that T(r T(2) but T1 T2 then T is not an onto linear transformation. (b) (A B) A-1 B-1 If A is invertible and r 20 then (rA) For all invertible matrices (AT) (A-1)r.

Solution

a. False

b.True

c.True

d.False

e.True

f.False

g.False

h.True

i.True

j.True