Question

1 4 bea linear/matrix transformation such that Let T: 3 Fi 1 4 1 T 1 1 C 6 h 3 Use the fact that T is linear to find the standard matrix [T of T and find T 1 Find a match for each of the following questions or choose NO MATCH if you can't find a match. What is the domain of T? What is the codomain of T? 4 4 How many rows does [T] have? How many columns does [T] have? 3 -1 2 1 What is the first row of [T]? [2-3-1 What is the second row of [T]? What is the third row of [T]? [011 What is the fourth row of [T]? [1-3 h True True or False? The range of T is a subspace of R. True or False? The kernel of T is a subspace of R4. Choose. Choose Find ALL values of h for which ker(T) is the zero subspace? Choose Find ALL values of h for which T not one-to-one? Find ALL values of h for which the range of T is equal to the Choose. codomain? Find ALL values of h for which T is onto (the codomain)? Choose. 2 s in the range of T when h -0. True or False? Choose 5 (In the exam you must justify your answer!)

Answer 1

-0-10-13-13-1- +223 0. T 2 2 El--E -2 1 6P 2 1 2 3 2 2 T 1 0 41 6 2 2 1 2

T El-8A-El- 0 T 1 1 3 +h-6) T 1 [T] 1 2 3 h-6 - 2x +3 j t 7 T

What i tte olomain of T 3 khat ib te lo dovaain vfT? Towh doen Jhave Hlo mant Colurons doen ] hawe hat i6 te first MOA T-2 3 17 khat Mar Lhal io the third IT] MoL [-1 3 h-6 Whal YoW Falbe Cibspane R I is a Te Tonte Putspace fR Fabe kernel ofT is

2 3 I 2 3 h-6 2 - 1 - 1 h- Ri-R3th2 RyRytha 2 - 1 -1 -1 0 0 8-1 - ) - 1 h-8 0 Valuen f h fos wliek ker(T) is Ite zemo faspace Valneo of h for Which T not One-o one bo Values of h Yapge of Tis ^fuul do the Codomain по Values of h Tis om h. Let b 5

When h0 TLe augmemtesl natrix i 2 2 3 2 | - 2 1 36 2 - 1 3 | 0 0 2. 0 -8 R3Ry 2 $2 -1 - 1 2 0 nue Tank LT yonlk 27 Henee 3 js in te Tamte of T shen h z0' 1