
2. Let M22 be equipped with the standard inner product. Determine whether u is orthogonal to...
2. Let M,, be equipped with the standard inner product. Prove. u is orthogonal W-span w,w,w) 3 -1 note: You must use some of the axioms in the definition of an inner product
2. Let M,, be equipped with the standard inner product. Prove. u is orthogonal W-span w,w,w) 3 -1 note: You must use some of the axioms in the definition of an inner product
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto the line spanned by the vector v. (b) Find W2, the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. u =(1,-1); v = (3,1) (a) wi = Click here to enter or edit your answer (0,0) Click here to enter or edit your answer (b) 2 = W2 orthogonal to...
4. Consider R³ with the standard inner product (i.e. the dot product). Let c{() (:} U = span 2 Find U+. (Write as a span of some set.)
2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of w = [1, 2,-1,2]T onto the span of ui-|1,-1, 2, 5]T and u2 [2,1,0,-]. Make sure you are working with an orthonormal basis for u span(u, u2 before you use the usual projection formula.
2. Consider R with the weighted inner product = [wn, u, tva, teal"). [ruh, t', talT and w Find the orthogonal projection of...
3. Let R be equipped with the inner product (x,y) = AX Ay, where A is the matrix shown below: TO-4 21 A = 3 2 LO 0 5) a.) (5 points) Let v = (1,-1,3). Find || V || 1 b.) (5 points) Let x = (2,3,0) and y = (-3,2,1). Are x and y orthogonal in this inner product space? Justify your answer
3. Let R3 be equipped with the inner product (x,y) = Ax. Ay, where A is the matrix shown below: TO A=13 LO -4 2 0 2 1 5) a.) (5 points) Let v = (1,-1,3). Find ||v||. b.) (5 points) Let x = (2,3,0) and y = (-3,2,1). Are x and y orthogonal in this inner product space? Justify your answer.
3. Let R3 be equipped with the inner product (x, y) = AX Ay, where A is the matrix shown below: TO -4 21 A = 3 2. LO 0 5) a.) (5 points) Let v = (1,-1,3). Find || V ||. UN b.) (5 points) Let x = (2,3,0) and y = (-3,2,1). Are x and y orthogonal in this inner product space? Justify your answer
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
1. If the vectors
and
are orthogonal with respect to the weighted inner
product
<
> =
, what must be true about the weights
?
2. Do there exist scalars k and m such that the vectors p1 =
2+kx+6, p2 =
m+5x+3 and
p3 = 1 + 2x + 3 are mutually
orthogonal with respect to the standard inner product on P2?
N 12 We were unable to transcribe this image= 1211 + Աշշ W1, W2 We were...
(1 point) Consider the complex inner product space C with the usual inner product Let -4i 4i and let w = span(vi,V2). (a) Compute the following inner products: (v.vi)- 2 (Vi, V2-12 (2. V)12 (b) Apply the Gram-Schmidt procedure to Vi and v2 to find an orthogonal basis (ui,u2l for W , u2=1112