EXPLAIN STEP BY STEP In Exercises 13 through 18 determine if the set of vectors S...
In Exercises 17-32, a vector u in R" and a subspace W of R" are given. (a) Find the orthogonal projection matrix Pw. (b) Use your result to obtain the unique vectors w in W and z in w such that u=w+z (c) Find the distance from u to W. 19. u = 2 and W is the solution set of the system of . equations X1 + X2 - X3 = 0 x1 - x2 + 3x3 = 0.
need help on number 13 Exercises 11-16. Represent each linear system in marrix form. Solve by Gauss elimination when the system is consistent and cross-check by substituting your solution set back into all equations. Interpret the solution geometrically in terms planes in R3. of 2x1 +3x2 x3 = 1 4x1 7x2+ 3 3 11. 7x1 +10x2 4x3 = 4 3x1 +3x2+x3 =-4.5 12. x1+ x2+x3 = 0.5 2x-2x2 5.0 x+2x2 3x3 1 3x1+6x2 + x3 = 13 13. 4x1 +8x2...
Step by step for #8 1) Given (1 2 3 1 0 11 1 5 2 1 A= -2 -5 -4 -1 1 ( 3 5 11 4 1 Find the basis and dimension for the row, the column spaces, and the null space NA Also, state the rank, the nullity of A 2) The subspace of W in R spanned by vectors u =(2.-2.1) v =(1,2,2) is a plane passing thru the origin. Express the vector w=(1,0.2) in the...
Provide a geometric comparison with the solution set of the second system of equations shown below. Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations shown below. X1 - X2 + 3x3 = -3 Xy - X2 + 3X3 = 0 2Xq + x2 + 3x3 = - 9 2 xy + x2 + 3X3 = 0 where the solution set...
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations) Question (7) Consider...
Determine whether the set w is a subspace of R3 with the standard operations. If not, state why. (Select all that apply.) W = {(x1, 1/X1, X3): X1 and xy are real numbers, X1 + 0) W is a subspace of R W is not a subspace of R because it is not closed under addition. Wis not a subspace of R because it is not closed under scalar multiplication. X
How do I do these linear algebra questions? The question is: Consider the Vector Space V and its subset W given below. Determine whether W forms a subspace of V. If your answer is negative then you must provide which subspace requirement is violated. (b). V is P5, the vector space of all polynomials in x of degree s5 and W is the set of all polynomials divisible by x – 3. (c). V is P5, the vector space of...
Determine whether the given set S is a subspace of the vector space V.A. V=C2(ℝ) (twice continuously differentiable functions), and S is the subset of VV consisting of those functions satisfying the differential equation y″=0. B. V=ℙ5, and SS is the subset of ℙ5 consisting of those polynomials satisfying p(1)>p(0)C. V=ℙ4, and SS is the subset of ℙ4 consisting of all polynomials of the form p(x)=ax3+bx.D. V=Mn×n(ℝ), and SS is the subset of all symmetric matrices.E. V=ℝ2, and S consists of...
Problem 7: Let S be the subspace of R' defined by the equation: x,+2x2-13 = a) Find an orthonormal basis for S and an orthonormal basis for S b) Find the vectors liE S and vES® such that the vector x = (2,1,-8/ can be written in the form x = 11 +-
?24) 1. To show that set of vectors of formm 2. (a) if A is invertible, list three different methods to solve equation Ax-b. b) Application each of above mentioned methods to solve is a subspace of a space of all 2x2 matrices. -x2 +2x3 =0 Find a matrik that reflects vectors in R' about yz-plane and then expand the length twice (2 0 3 2 7 Given set of vectors S=(1 1, 1-1, 1 .. D in R 10)...