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- In Problem ,use the vectors in the figure at the right to graph each of the following vectors. 3v + u - 2wFor question 6: Determine if the vector u is in the column space of matrix A and whether it is in the null space of AFind the coordinate vector [x]Bof x =| 3 || −5 | relative to the basis, | 4 | B= {| 1 || 0 || 3 | ,| 2 || 1 || 8 | ,| 1 | | −1|| 2 |}.
- If Ax = Bx for some nonzero vector x, then the matrices A and B must be equal.Question 3 Let the basis B = {v=(1.2.3), u=(2, 1, 2), w= (3.-3, 1)} andx=(3, 2,-1). 1. Write the coordinate vectors [x]g: [u]3Let A =[ 4 -1 2 , -1 8 3 ,1 -2 5 ] b=[1 ,-2,3] and initial vector x 0=[0,0,0,0] perform two itearation of the gauss seidel method
- deal with the problem of solving Ax = b when det A = 0.22.Suppose that, for a given matrix A, there is a nonzero vector x such that Ax = 0. Show that there is also a nonzero vector y such that A*y = 0.From the system x' = -x + 5y og y' = -y show that the vector function (top of picture) is a solution of the system only if (bottom of picture) is true.I need to solve this without using matrices. The components of a vector V in the basis B = (v1,v2) are (3,-2). Which are the components of the same vector in the basis C = (u1,u2), if v1 = 4u1-u2 and v2 = 4u1-3u2? Remember, no matrices.
- Find the coordinate matrix ofp = 4 − 2x2 + 3x3relative to the standard basis for P3,S = {1, x, x2, x3}.In Problems 21–26, decompose v into two vectors v1 and v2 , where v1 is parallel to w, and v2 is orthogonal to w. 25. v = 3i + j, w = - 2i - jFind the coordinate vector of ?=2−4? relative to the basis ?={?1,?2} for ?1 where ?1=3+8?, ?2=1+?.