Let B 1 ={u 1 ,u 2 } and B 2 ={v 1 ,v 2 } be the basis of R 2 in which u 1 =(2,2

Question

Let B1={u1,u2} and B2={v1,v2} be the basis of R2 in which u1=(2,2), u2=(4,-1), v1=(1,3), and v2=(-1,-1).
(a) use formula (14)* to find the transition matrix PB2—>B1 (Please show steps!! Thanks :)
(b) use formula (14)* to find the transition matrix PB1—>B2 (Please show steps!! Thanks :)
(c) confirm that PB2—>B1 and PB1—>B2 are inverse of one another
(d) let w=(5,-3). Find [w]B1 and then use the matrix PB1—>B2 to computer [w]B2 from [w]B1

*formula(14): [new basis | old basis] —row operations—> [ I | transition from old to new}

Explanation / Answer

a) https://s3.amazonaws.com/answer-board-image/a3807eab-2658-4ee2-8b2f-658128b41d0b.gif b) https://s3.amazonaws.com/answer-board-image/3aea6d52-e9ce-4368-8423-a0d46acad1f4.gif d) https://s3.amazonaws.com/answer-board-image/444338d0-faf4-4c24-a2c0-51ffbb9b29f9.gif

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

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