(The pink circles are for me; I\'m asked to do #5 and 7. You don\'t have to help

Question

(The pink circles are for me; I'm asked to do #5 and 7. You don't have to help me with both, I can figure out the other one on my own).

Thanks in advance!

i.)Ullowed by an owed by an isomorphism 72 PROBLEMS In Problems 1-4, a transformation T:R2 R2 is Cs. v, (2, 3), v -n: defined. Apply Theorem 1 to show that T is not W2 (0, 1) linear. 6. v1 (2, 3), va (0,1), l. T(x, y) (x 1, y 1) W2 (1,0) (1, 1), w2 (-1, 1) x, y) (xy, x 8. v (2, 1), w (1, 2) (3, 4), v2 (5,7), wi (-3, 1) (1,3), In Problems 5-10, find the 2 x 2 matrix A of a linear transformation T: R -r R2 such that 10. v, (4, 3), v2 (5, 4); w, (-3, 2), w. (-3, -4) T(i) Wi for i 1, 2 323 SEC, 7,2; Properties of Linear Transformations

Explanation / Answer

a

b

c

d

where a,b, c,d are arbitrary real numbers. Then T(v1)= Av1 and T(v2)= Av2 i.e. 2a+3b = 1, 2c+3d = 0, -a-b =0 and –c-d = 1.On solving these equations, we get a = -1,b =1, c = -3and d = 2. Therefore, the required matrix is A =

-1

1

-3

2

7. We have T(v1) = T(2,-1) = w1 = ( 1,1), T(v2)= T(-1,1)= w2 = (-1,1). Let A =

a

b

c

d

where a,b, c,d are arbitrary real numbers. Then T(v1)= Av1 and T(v2)= Av2 i.e. 2a-b = 1,2c-d =1, -a+b = -1 and –c+d =1. On solving these equations, we get a = 0,b =-1, c = 2and d = 3. Therefore, the required matrix is A =

0

-1

2

3

a

b

c

d

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.