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- Please explain each steps of part d, e, f in detail so that I can understandarrow_forwardSolve the following questions: Q1) Check whether the set W = {(2a + 5b, –a + b, 3a + 4b); a, b are real numbers } is a subspace of R3 or not.arrow_forwardThis is from section 1.3 "Homogenous Equations" out of the textbook titled "Linear Algebra With Applications". If you could provide step by step instructions in how to do these problems, I would be grateful. Thanks!arrow_forward
- please solve it as soon as possiblearrow_forwardPlease see imagearrow_forward1. a. b. x1 + x2 x1 2x1 T X2 Find the solution set of the following system of linear equations : 5x3 2x3 X3 || 3 1 0 What is the dimension of this set of solutions? Of what vector space is it a linear subspace? (R"?)arrow_forward
- Let y = 1 2 and u = 4 2 Write y as the sum of a vector in Span (u) and a vector orthogonal to u. y=y+z= (Type an integer or simplified fraction for each matrix element. List the terms in the same order as theyarrow_forwardLet A be an n x n matrix, let S = (ü, ü, u) be a set of non-zero vectors in R", and let U be a subspace of R" of dimension at least 1. Look at the expressions and phrases that follow. Select the ones that DO NOT make sense, because they either equate two different "types" of thing that can't be equal, use nonsensical notation, or try to perform an operation that is not defined. (For the computer programmers reading this, the question is essentially "find the type errors".) Warning: To clarify, you're not being asked which ones are true. You're being asked to identify which equations don't make sense. From the 11 choices, select all that apply "a basis of 5" "the solutions of the system of equations" im(A) (R" Ay for some FR") "the span of A" im(A) - (A#-5) "S spans U "the solutions of the matrix" im(A) {ER: Af=ÿ) null(A) = {A=0} 1 null(4)-(ER": Až=6) "U spans S"arrow_forwardIn each part, determine whether the vectors are linearly independent or are linearly dependent in P2. (a) 4 – x+ 4x²,4 + 2x + 2x², 4 + 6x – 4x? (b) 1+ 3x + 5x²,x + 4x²,4 + 6x + 5x²,2 + 5x – x²arrow_forward
- Please help with this:arrow_forwardShow how v is orthogonal to any linear combination formed by w1 and w2arrow_forward3. (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
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage