Let
W=x1,x2,x3,x4()|x1+x2=x3+x4{}. Is W a subspace of R4? Justify your an
Let W=x1,x2,x3,x4()|x1+x2=x3+x4{}. Is W a subspace of R4? Justify your answer.
Let W=x1,x2,x3,x4()|x1+x2=x3+x4{}. Is W a subspace of R4? Justify your answer.
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Consider the subspace W C R4 given by X1 X2 W = ER4 X1 + x2 + x4 = 0 and x2 + x3 + x4 = 0 X3 X4 = Find an orthonormal basis H {h1, h2, h3, h4} for R4 with the property that hy and h2 are elements of an orthonormal basis for W, where orthonormality is defined with respect to the dot product on R4 x R4.
Consider the subspace W C R4 given by X1 X2 W = ER4 X1 + x2 + x4 = 0 and x2 + x3 + x4 = 0 X3 X4 = Find an orthonormal basis H {h1, h2, h3, h4} for R4 with the property that hy and h2 are elements of an orthonormal basis for W, where orthonormality is defined with respect to the dot product on R4 x R4.
Let V = R4 and let T : V → V be defined by T x1 x2 x3 x4 = x1 −x3 x2 + x4 x1 −x3 −x2 −x4 . (a) Show that T is a linear transformation. (b) Show that T(T(v)) = 0 for v ∈ V . (c) Show that imT = hT(e1), T(e2)i. (d) Show that...
LINEAR ALGEBRA 9 9 1. (16 pts.) Consider the set B = {V1 = (1,1,-1, -1), V2 = (2,2, -3, -1), V3 = (1, -1,1, -1)} in R4. Show that B is a basis of the subspace V = {x1 + x2 + x3 + 24 = 0} of R4.
4. (a) L ,DER et a i. Let U1 be the set of solutions for the equation For which values of a and b is U1 a subspace of R4? ii. Let U2 be the set of solutions for the equation For which values of a and b is U2 a subspace of R4? iii. Let U3 be the set of solutions for the equation For which values of a and b is Us a subspace of R4? Justify your...
Problem 2. This is adapted from our textbook. Let X -[x1,x2, x3,x4 be a set of four monetary prizes, where 0 < x1 < x2 < 13 < x4. Stowell claims he is an expected utility maximizer. He is observed to choose the lottery π-(1, 1, 1, ) over the lottery π,-(0Ί, , Ỉ ). Based 1 11 7 4 24 24) Based on that observation, can you conclude that he is truly an expected utility maximizer, as he [10...
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the standard matrix representation A of T b.) find the basis of Col(A) c.) find a basis of Null(A) d.) is T 1-1? Is T onto?
Solving Systems of Linear Equations Using Linear Transformations In problems 1-5 find a basis for the solution set of the homogeneous linear systems. 2. X1 + x2 + x3 = 0 X1 – X2 – X3 = 0 3. x1 + 3x2 + x3 + x4 = 0 2xı – 2x2 + x3 + 2x4 = 0 x1 – 5x2 + x4 = 0 X1 + 2x2 – 2x3 + x4 = 0 X1 – 2x2 + 2x3 + x4...
In each part, determine whether the equation is linear in x1, x2, and x3. (a) x1 + 5x2 − √2 x3 = 1 (b) x1 + 3x2 + x1x3 = 2 (c) x1 = −7x2 + 3x3 (d) x−2 1 + x2 + 8x3 = 5 (e) x3/5 1 − 2x2 + x3 = 4 (f ) π x1 − √2 x2 = 71/3
2 = -4 and x3 = 0, with p = 1 and W = span{x1, X2, X3}. 4) Let x1 = -2, X2 3 (a) W is a subspace of R". What is n? (b) Find a basis for W. (c) Isp EW? (d) Give a geometric description of W.