4.4.13. Find a basis for the orthogonal complement of the following subspaces of R³: 5z = 0; (b) the line in the direction (-2, 1, 3); (c) the image of the (a) the plane 3x + 4y 1 -1 3 matrix -2 2 1 (d) the cokernel of the same matrix. 1 4 2 0 −1 2

Q: B = (f1. f2. f3) is a basis for R2[r]. If the change of basis matrix from B (1 2 3) Seal=] is (1 3 4…

A:

Q: 11. Find a basis of the following subspace of R4. all vectors of the form (a, b, c, d) where a + b –…

A: The solution is given as

Q: 11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a +…

A: To find: Basis of W={(a,b,c,d) | a+b-c+d=0}.

Q: Dases C= and E on R3, (i) Find the vector v3 of R' whose component vector with respect to C is [v3]c…

A:

Q: Find the coordinate vector [x] of x relative to the given basis B = ={D₁, D₂, D3}. 1 b₁ = -1 b₂ = 4…

A: we will find the required.

Q: 10. For a new basis system the two basis vectors are E',E,+E₂+E, E'=E,-E, where E is 1 1 the…

A: ​ ​

Q: 1 2 . Let uj = |0 u2 = 4 and u3 = 1 1 1 -2 (a) Show that {u1,u2, U3} is an orthogonal set.

A: "Since you have asked multiple question, we will solve the first question for you. If you ant any…

Q: s) Determine if these vectors for a basis for R³: linear combination of these vectors. 0·0-0--0- and…

A:

Q: -5 Given v 9 -3 find the coordinates for v in the subspace W spanned by

A:

Q: The orthonormal basis of the subspace spanned by the vectors is (Use a comma to separate vectors as…

A:

Q: T2. Use the idea in Exercise T1 and matrix multiplication to deter- mine whether the polynomial p =…

A:

Q: 9. V =|-1 Write the vector as the linear combination of the basis vectors 3 4 and u, =|- 3 u, = 2…

A:

Q: 1 3 -1 - 7 Let P = -3 -5 v = 2 V2 and v3 = 3 . Complete parts (a) and (b). 4 1 5 a. Find a basis…

A: Consider the provided question, According to you we need to solve only part (b).   Given…

Q: 2. Consider the subspace im(A) of Rº, where 1 1 A = | 1 1 3 Find a basis of ker(A"), and draw a…

A: Given matrix A=111213 AT=111123