Given v = U₁ = 0 find the coordinates for v in the subspace W spanned by 1 [3] 0 -1 V = -9 3.33 -3 7 3 5 1 4 Note that u₁, 2, 3 and 4 are orthogonal. 1 , U₂ = , uz = U1 + -0.275 11 [3] -1 4 -7 and u4= u2+ -0.776 [3] -3 1 1 u3+ 2.818 us

Q: O Linear subspace L is given by the equations 2r1 + r2 + 3r3 - 14 = 0 = 0 3r1 + 2r2 – 2r4 3r1 + 12 +…

A: Let AX=0 213-1320-2319-1x1x2x3x4=000R2→R2-32R1 , R3→R3-32R1…

Q: give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a.…

A:

Q: 1 -3 0 Let v¹ 3 1 ,w= -5 and determine if w is in the subspace of R³ -2 2 generated by v¹ and v².…

A:

Q: Find a basis for the indicated subspace of R³. The line of intersection of the planes with equations…

A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

Q: What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors a₁ =…

A:

Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

A:

Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: 1 Given v = -1 4 find the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 u1 = 1 , u2 =…

A: The vectors u1, u2, u3, u4, u5 are orthogonal. Therefore, ui·uj=0, for i≠j. Consider the given…

Q: The vector x is in a subspace H with a basis B = {b₁,b₂). Find the B-coordinate vector of x. 2 b₁ =…

A: We are given that           b1 = (2, -3)t          b2 = (-1, 5)t        Now, x is in H with the…

Q: Q: Let W, ={(a, B.Y, 8): a=y+28, y= 28} and W2 {(a, B.Y, 8):a-y-0} be two subspaces of V,(R). Find a…

A:

Q: Find a basis and state its dimension for the following subspace in Rª 3r+ 6s-t 6r-28-2t -9r+ 5s + 3t…

A: Given that 3r+6s-t6r-2s-2t-9r+5s+3t-3r+t: where r,s,t∈ℝ

Q: 2 -1 3 -1 -3 -2 -1 -6 -7 2 4 -8 6. Find bases and dimensions for the four subspaces associated with…

A:

Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

A:

Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

A:

Q: Given v = find the coordinates for v in the subspace W spanned by -7 u1 = and uz -1 -28 Note that uj…

A:

Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

Q: Let W be the subspace spanned by the given vectors. Find a basis for WL. w1 = 1-18-2, w2 = 01-71…

A:

Q: Let W be a subspace spanned by the u's, an

A: Given, W be a subspace spanned by u's, and write y as the sum of a vector in W and a vector…

Q: 5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³…

A:

Q: Help find a basis for the subspace spanned by the given vectors provided attach. Whats the dimension…

A:

Q: 2. The subspace in R3 is a plane whose equation is x+y+z=0 x-2=0 x-2y+z=0 (a) (b) 2-0 (c) y-2--0…

A:

Q: 1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes,…

A: Given v1 = 10-2v2 = 311v3 = 612w = 321 The equation x1v1+x2v2+x3v3=w will have a solution if the…

Q: Given that V1 = 5 3 V2 = 2 } V3 = 3 7 " 11 10 For what value(s) of h will y be in the subspace of H…

A:

Q: Find the closest point to y in the subspace W spanned by v₁ y = 5 1 1 15 - 1 1 - -1 2 V2 - 3 1 0 2…

A:

Q: Let v₁ = O 1 5, V₂ = No Yes -2 -7 13 and w= - 3 -6 19 Is w is in the subspace of R³ generated by v₁…

A:

Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

A:

Q: Let W be the subspace spanned by u₁ and u2, and write y as the sum of a vector in W and a vector…

A: Let W be the Subspace Spanned by u1 and u2,Write y as the sum of a vector in W and a vector…

Q: Show that the given set V is closed under addition and multiplication by scalars and is therefore a…

A:

Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

A:

Q: 2 Find bases and dimensions for the four subspaces associated with A and B: A = 1 2 4 and B= = 1 24…

A: We will find the bases and dimensions.

Q: -8 -5 -1 6 -4 --- U₁ = -5 -6 -7 -10 1 -18 Compute the distance d from y to the subspace of R4…

A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

Q: Let W be the subspace spanned by u, and u₂, and write y as the sum of a vector in W and a vector…

A:

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors u. (You may assume…

A: To find the orthogonal projection of v onto W:

Q: -8 Given v = -7 find the coordinates for v in the subspace W spanned by -1 4 -3 u1 3 , U2 and U3 -17…

A: