B = = v= -6 3 6 109 1 -37 -20 -2 -2 -2 1 2 is an orthogonal basis of Rª. Find [v] Fo

Q: Show that ?? = {(1,2,3), (−1, −1,1), (5, −4,1)} is an orthogonal basis of ℝ3, and use the Fourier…

A: Definition: A subset of a vector space V is linearly independent, if  Theorem: If is a orthogonal…

Q: the basis of P2 cons tive to B.

A: Introduction: For some n, consider V to be a subspace of Rn. A basis for V is a collection of…

Q: The set F = {1+t,t +t, 1+2t+t2} is a basis for P₂. Find the coordinate vector of p(t)= 3 +t-4t²…

A:

Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: Using the scalar form of the table 1 3 2 3 1 1- - a 1 6 = 6+ a 5 4-a 2 -2 5 12 19 to determine the…

A: Step 1: Write the matrix A in scalar form. A = [[1, 3, 5, 6 + a], [2, 3, 4 - a, 2], [1, 1 - a, - 2,…

Q: The set B={1-1², -2t-t², 1-t-t²} is a basis for P₂. Find the coordinate vector of p(t)= -3-11t-2t²…

A:

Q: The set B = • {1+t², −t+t², 1 + 2t+t²} is a basis for P₂. Find the coordinate vector of p(t) =…

A:

Q: Consider the following two ordered bases of R²: [id] B = [id] = {(-1,-1), (-3,-2)}, a. Find the…

A:

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: 2 Determine whether the vectors form a basis for R*. (You may use any relevant theorem that we have…

A: A basis for a subspace S of Rn is a set of vectors in S that is linearly independent and is maximal…

Q: 127 (68) -100 -4 23 B = v= 27 is an orthogonal basis of R³. Find [v]⁄·

A: (.) Given orthogonal basis is,           and  vector (.) Orthogonal basis: A basis  is called an…

Q: Explain why S is not a basis for P2. S = {1, 7x, -6 + x², 2x} O sis linearly dependent. O s does not…

A:

Q: Let ----0-- -2 = Show that {V₁, V2, V3} forms an orthogonal basis in R³. Express W= as a linear…

A:

Q: Explain why S is not a basis for P2. S = {1, 6x, –9 + x², 7x} O Sis linearly dependent. O S does not…

A:

Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

A:

Q: The set B = {1+t², -t+t², 1+2t+t²} is a basis for P₂. Find the coordinate vector of p(t) = 5-6t+13t²…

A:

Q: -10 [x] B = 10 -10 25/24 2,0 -35/24 Find the coordinates of x in the ordered basis B = (a, b). 2,0…

A: Since  in the usual basis  has coordinates, . So, to obtain its coordinates in the basis,  , where

Q: Let [3³] Ai B , where B = {b₁,b₂} is a basis in R². Then 3 B 061+06₂

A:

Q: Show that {u₁, u2} is an orthogonal basis for R². Then express x as a linear combination of the u's.…

A: Given:u1​=[2−6​],u2​=[124​],x=[2−2​]  Step 1: Check OrthogonalityTwo vectors u1​ and u2​ are…

Q: Explain why S is not a basis for P₂. S = {1x, 1x², −1 − 5x + 6x²} OS is linearly dependent. OS does…

A:

Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

Q: ?:R3 →R2,with? ?,?,? =(?+2?+3?,4?+?−2?) Find a basis for the image and state its dimension.

A:

Q: Show that B = {v1, v2, v3} is an orthogonal basis for R3: v1 = (3,−3,0), v2 = (2,2,−1), v3 =…

A:

Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x², 8x} S is linearly dependent. O s does not…

A:

Q: The set B= {1- 21-,1-t-t) is a basis for P,. Find the coordinate vector of p(t) = 5+ 13t-121…

A: 4 7 1

Q: - --- Let B = Is Ba basis ofR ? Justify and x = %3D 2 3 3 your answer. If yes, compute xR [x]

A: