Question: Let A = [al a2 ... an be an m xn matrix. If the set of vectors { a1, a2, . .., an } in

Let A = [al a2 ... an be an m xn matrix. If the set of vectors { a1, a2, . .., an } in RM is linearly independent, which of the following is/are true? (select all that apply) The matrix equation Ax = 0 has free variables. The rank of A is equal to n, The homogenous system Ax = 0 has only one solution. n'm All columns of A are pivot columns

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Please answer the given question in detail: Let { Al, A2, . .., Ak} C Rm be a linearly independent subset of vectors. Suppose Ak+1 E RM is not in the sub- space spanned by the vectors Al, A2, ...,...

\fAns : 1 [ ] v = 2 , w= 1 , u= 2 1 2 3 Let a , b R such that av+bw=o >a 2 +b 1 = 0 1 2 0 [ > 2 a+ b = 0 a+2 b 0 >2 a+b=0 a+2 b=0 Solve these two equation we get a=0 , b=0 Thus { v , w } is linearly...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Problem 1. Let A be an invertible n X n matrix. If A is diagonalizable, prove that A1 is diagonalizable. Problem 2. Let A be a 2 X 2 matrix with exactly one real eigenvalue A, and assume A has...

. Consider the matrices to answer the following parts: 1 1 0 12 4 0 57 0 2 14 A : 1 O 1 B : 1 6 1 4 1 13 3 76 2 3 5 27 2 31 71 1 740 (a) Find A_1, if possible. (b) Use a \"simple\" computation to nd...

Ryan Ren Assignment Homework 2 due 09/14/2017 at 02:15pm PDT 1. (1 pt) Compute the following product. \u0014 \u0015\u0014 \u0015 \u0014 5 0 4 7 4 = 0 7 1 7 7 Math4A-02-M17-Wen \u0015 Answer(s)...

1 1. (6+4+4+6) Let P3 denote the vector space of all third degree or less polynomials. (a) Find two linearly independent vectors in P3 that interpolate the data points (1, 2), (2, 1) and (3, 2). (b)...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

3 Systems of differential equations In Sections 3.8-3.10 we will reduce the problern of finding all solutions of (1) to the much simpler algebraic problern of solving simultaneous linear equations of...

Interest on Zeroes Snowflake Corporation needs to raise funds to finance a plant expansion, and it has decided to issue 25-year zero coupon bonds to raise the money. The required return on the bonds...

3. Calculate the Poynting vector of a wave propagating in coaxial cable. The electric and magnetic field are given by: E(s, o, z, t) = A cos(kz - wt) S -, B(s, o, z, t): = A cos(kz - wt) -$. FIGURE...

Career Cemer Trading Olallenge Go Back In a situation where a Canadian exporter is uncertain about winning a large commercial contract denominated in Mexican Pesos ( MXN ) , which hedging method...

Required information Use the following information for the Quick Study below. [The following information applies to the questions displayed below.) Brodrick Company expects to produce 20,500 units...