Question

Fill in the blank and explain why the following statement is true: "If A is an mxn matrix, then the columns of A are linearly independent if and only if A has____ pivot columns.

Expert Answer

1 Rating

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by students like you.

Q: pls explain to me step by step and dont skip any steps. Thanks

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want an...

Q: Differential equations. Find the particular solutions to the given systems of equations. Please refe...

A: (a) The differential equation is given as

Q: pls explain to me step by step and dont skip any step. i will rate your answer immediately. thanks a...

A: To analyze the given non-linear system at its critical point(s)

Q: Mechanical Vibrations (differential equations) A mass weighing 4 pounds is attached to a sping whose...

A: Let m be the mass attached, k be the spring constant and let b be a positive damping constant.Then, ...

Q: I need help with this question. Thanks!

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Solve the first order differential equation using any acceptable method. (6x+1)y2 dy/dx+3x2+2y3=0,  ...

A: Given the differential equation isNow separate the variables as follows

Q: Find the critical points and sketch the phase portrait of the given autonomous first order different...

A: Consider the provided autonomous first order differential equation.

Q: Solve the systems of linear equations 2x + y = 7 x-y = 3

A:  To solve the system of linear equation. 

Q: Subject: Set Theory

A: • Transitive relation means that, whenever an element a is related to an element b and b is related ...

Q: Abstract Algebra Proofs: Help a desperate college student out please.

A: Click to see the answer

Q: pls explain to me step by step and dont skip any steps. thanks

A: To prove that the system is asymptotically stable under the given conditions.

Q: How many ways can you choose 5 out of 10 friends to invite to a dinner party?

A: To solve the problem of combinations (selections) in the given scenario.

Q: See attachment for question.

A: Click to see the answer

Q: the book is "First Course on Fuzzy Theory and Applications"

A: Consider the provided fuzzy bunch of functions:

Q: Mechanincal Vibrations (Differential equations) When a mass of 2 kilograms is attached to a spring w...

A: The differential equation for equation of motion is given by,

Q: Find the simple interest paid on a $470 loan at 6.9% annual interest for 3 months

A: Given:The principal amount (P) is $470.The rate of interest (R) is 6.9% per year.The number of terms...

Q: Find the point of intersection of the given pair of straight lines x - 4y = -2 x + 2y =4

A: Simplify the equation x-4y=-2 as follows.

Q: How do you do 32 and 33

A: To find the number of solutions of the given equation involving the lcm of two positive integers.

Q: Pls explain to me step by step. Pls dont skip ay steps. thanks

A: Suppose P=(x0,y0) is an critical point of the system x\'=f(x,y) , y\'=g(x,y),and that f and g are di...

Q: 6.3.22 How many permutations of the letters ABC DEF GH contain D the string AB, DE, and BED?

A: The given letters are ABCDEFGH.Obtain the permutations as follows.

Q: I needed help solving this problem. Thank you.

A: Hey, since there are multiple subparts posted, we will answer first 3 questions. If you want any spe...

Q: O= {-32, -8, -2, -1, 1, 4, 16, 64) N= {1.2.4.8} u- -32, -8, -2, -j, 1, 2, 1002, 8, 1004, 10003, 64) ...

A: Here, We are answering first four part of the question,We have given set is as follows:

Q: Consider the Linear programming below: Max 3x1+2x2 subject to  2x1+x2>=6 x1>=2 x1,x2>=0 Det...

A: Consider the Linear programming below:Max.  3x1+2x2Subject to 

Q: Abstract Algebra

A: To find non-negative representations under the given conditions

Q: 6.20 (Nine Chapters 6.27) Now given a person carrying cereal through three passes. At the outer pass...

A: To convert the word problem into an equation for the original amount and solve it.

Q: Need help with Differential Equations homework. Help with 4 problems. Apply Laplace Transform to fin...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Let x be  a set containing 20 elements. Use the multiplication princple to compute |p(x)|, the size ...

A: It is given that, the number of elements in the set X has 20.The power set P(X) of a set X is the se...

Q: Prove that Z ≈ E*, where Z is the set of integers and E* is the set of positive even integers.

A: To prove:

Q: Use the approach in Gauss’s problem to find the following sums of arithmetic sequences (do not use f...

A: To find the sum of the given arithmetic sequence using Gauss's approach.The given sequence is 1+3+5+...

Q: I need help for problem 1. Thanks!

A: Suppose there are two limits for f(x) as x tends to a named as l and m.Them, the uniqueness of limit...

Q: I only need the explanation of question number 5, 6, and 7. I do not know how to do it.

A: Hey, since there are multiple questions posted, we will answer first question you asked for. If you ...

Q: 3.17 Theorem Let {sn} be a sequence of real numbers. Let E and s* have the same meaning as in Defini...

A: As per norms, the first question is not answered as it carries points,. Questions 2,3 and 4, concern...

Q: 8. Suppose a vending machine accepts $1 bills, $1 silver coins and $1 gold coins, $3 bills and $3 go...

A: 8.a. To find the recurrence relation for the number of ways to deposit n dollars in the vending mach...

Q: How do you solve 2(9+6^x+1)=100

A: Given:The equation is 2(9+6x+1) = 100. 

Q: (Linear Algebra) For each linear operator T on V, find the eigenvalues of T an an ordered basis B fo...

A: First, we calculate its standard basis:Its calculation is shown on the board

Q: 5.2.6        Discrete Mathematics A) determine which amounts of postage can be formed using just 3 ...

A: B)Known fact:Base step: Show it is true for first case, usually n =1.Induction step: Show that if n ...

Q: Chapter 1 Section 1.2 19. A section of a gear is shown. Given the formulas below and the circular pi...

A: Formula used: 

Q: Section 1.2 Chapter 1 0.625 0.625 -RO. I 25 0.625 0.625- 0.625 15. A manufacturer must describe a di...

A: In the given diagram of CNC, the x-coordinate and the y-coordinate are the horizontal and vertical d...

Q: Abstract Algebra. Please explain everything in detail.

A: To discuss the reason why the three given functions fail to satisfy the properties of a Euclidean no...

Q: 5. Sixteen people on a softball team show up for a game. a) How many ways are there to choose 9 play...

A: (a)Total number of people that show up for game is 16.Therefore, number of ways for choosing 9 playe...

Q: Subject: College Geometry (Proofs)Book: Euclidean and Non-Euclidean GeometriesI could really need so...

A: Click to see the answer

Q: Abstract Algebra. Please explain everything in detail.

A: To describe all the field automorphisms of the given field.

Q: Use Laplace Transforms to find the solution to the initial value problem: y"-6y'+9y=t2e3t, y(0)=2, y...

A: Given:The initial value problem is y" - 6y' + 9y = t2e3t, y(0) = 2 and y’(0) = 17.

Q: the book is "First Course on Fuzzy Theory and Applications"

A: As per norms the first three parts a),b) and c) are answered. To determine the various fuzzy propert...

Q: An experiment consists of tossing a coin seven times and observing the sequence of heads and tails1)...

A: Given:An experiment consists of tossing a coin seven times and the outcomes are the sequence of head...

Q: 5.2.6          Discrete Mathematics (I filled in as much as I could) A) determine which amounts of ...

A: (A)We are given that the postage can be formed by using the stamps of just 3-cent and 10-cent only,S...

Q: Z is a complex variable z=x+iy  question attached as photo

A: The function is given as

Q: Abstract Algebra. Answer in detail please.

A: There are two aspects of the problem: first to show that any quadratic extension of R is isomorphic ...

Q: How much do you need to invest at the beginning of each of the next 60 months in order to have a val...

A: Since the given amount of $100,000 is deposited at beginning of each month, it is annuity due.Then c...

Q: pls explain to me step by step. thanks

A: To exponentiate the matrix tA, A as given, using the special properties of A.