MATH 2211 Quiz: Quiz11Spr11mt210Sample1Ans
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T(a + b) = (a + b) (a + b)t. = a at + b bt. Thus, t is linear. (b) consider m2 2 with the standard basis: {[ 1 0. Let a = [ a b c d ] a at = [ so that t . 0 b c a b c d. Then we get t : r4 r4. 0 1 ]}. c b where the standard matrix of t is. The range of t is given as x2 which implies that. : x2 r range of t = {x2[ 1 0 ] : x2 r} . 1 0 ]} is a basis for the range of t. Thus, the set {[ (c) note that the null space of t is null t = implies that kernel of t = {x1[ 1 0. 0 1 ] : x1, x2, x4 r} .
