suppose a line L in R2 contains the unit vector u=(u1). Find thematrix A of the linear transformation T(x)=refl(x). Givethe entriesof

(u2)

A in term of u1 and u2. Show that A is of the form (a)(b), wherea^2+b^2=1

(b)(-a)

answer

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Tod ThielLv2

8 Aug 2019

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let z bea fixed angle . if x belong to R2, let L(x)be the element of R2obtained by rotating x thru the angle z .

assumeL:R2-R2 is linear .

letu1=e1, u2=e2.

thenu1,u2 form a basis for R2 .

find aformula for L(x)

hint:first determine v1=L(u1) and v2=L(u2)

I think B was the best answer..

Because an indexed set {v1,...,vp} of teo or more vectors, with not being v1 zero vector, is linearly independent if and only if some vj is not a linear combination of the preceding vectors, v1,...,v(j-1)

but its answer is D

plz explain the answer using the <Linearly Independent sets Theorem>

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suppose a line L in R2 contains the unit vector u=(u1). Find thematrix A of the linear transformation T(x)=refl(x). Givethe entriesof (u2) A in term of u1 and u2. Show that A is of the form (a)(b), wherea^2+b^2=1 (b)(-a)

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suppose a line L in R2 contains the unit vector u=(u1). Find thematrix A of the linear transformation T(x)=refl(x). Givethe entriesof

(u2)

A in term of u1 and u2. Show that A is of the form (a)(b), wherea^2+b^2=1

(b)(-a)