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- Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]arrow_forwardFor problem 6. Please help me the following: -For 6a and 6c. I have done the proof. Please only give me the two examples for each. - Please help me solve 6b. Thank you very much!arrow_forwardFor this question, Figure 3.4 as referenced in the question is inserted in the other image attached to this problem.arrow_forward
- 3. (a) Let A = (b) Let A = 1 1 0 1 1 1 0 1 1 1 1 combination of the column vectors of A, with coefficeints x1, x2, and x3. (c) Now generalize part (b) to the case where A is m × n. That is, show that if A is an 1 1 0 1 1 1 1 0 1 1 1 18 - What are the row vectors and column vectors of this matrix? 9 arbitrary mx n matrix and x = m and let = X1 x2 x 3 X1 x2 In the columns of A, with coefficients x1, x2,., n. be a vector in R³. Show that A is a linear 2c1 c₂ + c3, and let (d) Suppose that A is a 4 × 3 matrix, and let c₁, c2, c3 be the column vectors of A. That A [C₁ C₂ C3]. Suppose that be R4 is the vector 6 = 20₁ [ci is, is in R", then A is a linear combination of 9 X1 = X2 . Show that Aỡ = b is consistent by finding a solution to the system.arrow_forward(4) Linear subspace L is given by the equations 2r1 + 12 + 3r3 - 14 3r1 + 2r2 – 2r4 3ri + 12 + 9r3 - 24 = 0 = 0 =0 Find equations describing the orthogonal complement L.arrow_forwardHi, I need help with this Linear Algebra problem, please. I've tried 2.538, -10.392, & -1.165, but that doesn't appear to be correct. Any help is greatly appreciated. Thank you!arrow_forward
- Assume that you are given a set of points and you want to find the regression line for this data. In other words, you are given a linear system Xa Y with no solution and you want to find a vector a such that Xa is the vector in the column space of X closest to Y in the Euclidean norm. Explain how to solve this problem using a QR factorization of X.arrow_forwardI only need help with problem 10. Thank you.arrow_forwardneed help in matrix algebra. This is what I got but its incorrect.arrow_forward
- 1. (a) Find the matrix P that multiplies every vector (x, y, z) E R³ to produce the vector (3x+2y+z, 5y- z, 8x). Also find P-1. (b) Find the matrix P that multiplies every vector (x, y) E R2 to produce (5x-4y, - 2x, 3y - 2x) = R³arrow_forwardMust solve all three parts. Don't solve only one or two parts. Else skip it and leave it for others to do.arrow_forward1arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage