Find the orthogonal projection of 0 0 onto the subspace V of R¹ spanned by -1 1 1 -1 -1 -1 -1 -9 0 projy(v)= 1 -1 and -1 -1 1 1

Q: Find a basis for the subspace of R3 spanned by S = {(2,3, -1), (1,3, -9), (0,1,5)}

A:

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A:

Q: Find the Kernel and Range of the linear transformation L : R^3 → R^3 defined by L(x) = (x3, 0,…

A: In linear algebra, the kernel of a linear transformation is also known as the "null space." Given a…

Q: The union of two subspaces of a vector space is not necessarily a subspace.

A:

Q: If v1 and v2 are in R" and H=Gen{v1, v2}, then H is a subspace of R" Justify

A: Given that : and are in  Let Now, we  have to recall  the definition of subspace of a…

Q: Q4(a) Define the null space of an m x n matrix A and prove that it is a subspace of R"

A:

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -9 -4 -8 8 20 NHAW…

A:

Q: Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector…

A: The given set is a11b | a, b∈K. It is known that any subspace should contain the identity element.

Q: Find the closest point to y in the subspace W spanned by V₁ and V₂ 2 2 - 1 y= a. 3/6 -2/6 丽··· -1/6…

A:

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

A:

Q: 2. Let P3(R) be the vector space of all polynomials of degree 3 or less (and the zero polynomial).…

A:

Q: Consider the following. W = {(3t, t, -t): t is a real number} (a) Give a geometric description of…

A:

Q: Find the orthogonal projection of the vector [ 49 49 49] onto the subspaces of R3 spanned by [2 3…

A: We have to find the orthogonal projection of the vector  onto the subspace of  spanned by  and .

Q: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

A:

Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: -2 an orthonormal basis of the subspace spanned by the vectors 121C

A:

Q: Find the projection of the vector v onto the subspace S. 0 0 1 0 1 0 S = span V = 1 1 -1 - 1 1 - -1…

A:

Q: Find the orthogonal projection of 0 0 -9 0 onto the subspace V of Rª spanned by -1 -1 -1 proj, (v) =…

A: Let V be the vector space spanned by v1,v2,v3,.....vn. The projection of v onto V is obtained as,…

Q: Determine the dimension of the subspace of R consisting of all XeR* such that x1 + 2x, = 0 and X3 –…

A:

Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: X1 ER* satisfying the X3 X2 6. Show that the set of all vectors XA equations 3x1 - 2x2- X3-4x4 = 0…

A:

Q: Find a basis of the subspace V = 1 2 (-1) span{ -{() () · 0)·()} (3). -3 4 5 2 2 4 2

A: NOTE: Refresh your page if you can't see any equations. . write all four vectors in the matrix A

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (7) 0 -8 v= 0 0·00 ||

A:

Q: Let P, be the vector space of polynomials of degree at most 4. (a) Let W1 be the subset of P…

A:

Q: Find the orthogonal projection of v = projy(v) = [8] -25 H -7 onto the subspace V of R³ spanned by…

A:

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw(7) = = -15] -8 v = -16…

A:

Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: Find the orthogonal projection of x³ € P3 onto the subspace Span (1, 1 + x, 1 + x²). Justify your…

A: Here we have given a vector space of  onto the subspace…

Q: Find the orthogonal projection of onto the subspace W of Rª spanned by projw() = v= 4 -2 -13] 3 15…

A:

Q: Consider the subspace 3 12 3 -2 U = span{ 7 -2 -7 3 6. of R4. Create a basis 3 -2 { 3 -2 ,x} -3 for…

A: Consider the provided question, Consider the subspace U=span-3-27-7, 12-2-73, 3-2-46 of R4.Create a…

Q: Find the orthogonal projection of v= [15 8 0] onto the subspace V of R^3 spanned by [-1 -2 -2] and…

A: