Question: If A is a square matrix, show that det A = 0 if and only if some row is a linear combination of the others.

If A is a square matrix, show that det A = 0 if and only if some row is a linear combination of the others.

Step by Step Solution

★★★★★

3.52 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We have det A 0 if and only if A is not invert... View full answer

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

Document Format (1 attachment)

Word file Icon

950-M-L-A-L-S (6527).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let A be a square matrix that can be partitioned as where P and S are square matrices. Such a matrix is said to be in block (upper) triangular form. Prove that det A = (det P)(det S) o S

Q:

Mark each of the following statements true or false: (a) For all square matrices A, det(-A) = -det A. (b) If A and B are n n matrices, then det(AB) = det (BA). (c) If A and B are n n matrices whose...

Q:

Let A be a nonsingular square matrix. (a) Prove that the product of the singular values of A equals the absolute value of its determinant: 1 2 ... n = |det A|. (b) Does their sum equal the absolute...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

Answer the questions below relating to linear algebra (three parts). Please make sure to easily/accurately answer all the question parts. Find the general solution of the system whose augmented...

Q:

1) Give one example of a non-zero matrix A with at least 15 rational entries where the number of rows is larger than the number of columns and its row reduced echelon form. You must use your CSU ID...

Q:

1) Give one example of a non-zero matrix A with at least 15 rational entries where the number of rows is larger than the number of columns and its row reduced echelon form. You must use your CSU ID...

Q:

10Mail - Cl G Google Attachn W MAT 35 Search| Project t S Project Home D2L Online S D2L 3-3 MAT Zy Sect X D2L Project S Project D2L Project Project *MAT35( + X -> C a...

Q:

5. (a) Let A be a square matrix. If det A 6= 0, how many solutions does the equation Ax = 0 have? (b) Let B be a 3 3 matrix such that the entries in each row of B add up to 0 (i.e., bi1 + bi2 + bi3 =...

Q:

1. a. What detriment, if any, was sustained by the nephew? b. What benefit, if any, was secured by the uncle? c. As a matter of law, do we need to inquire into the uncles benefit? Explain. 2. Lampley...

Q:

Vaughn Inc. has decided to purchase equipment from Central Michigan Industries on January 2, 2014, to expand its production capacity to meet customers demand for its product. Vaughn issues an...

Q:

5. People feel shy to express their ideas because of the fear of being ridiculed. What can you do prevent such an atmosphere?

Q:

YOU BE THE JUDGE WRITING PRO BLEM John and Susan Verba sold a Vermont lakeshore lot to Shane and Deborah Rancourt for $115,000. The Rancourts intended to build a house on the property, but after...

Q:

A certain forest is divided into three height classes and has a growth matrix between harvests given by If the price of trees in the second class is $30 and the price of trees in the third class is...

Q:

In Example 1, what must the ratio of the prices p2: p3: p4: p5: p6 be in order that the yields Yldk, k = 2, 3, 4, 5, 6, all be the same? (In this case, any sustainable harvesting policy will produce...

Q:

For the optimal sustainable harvesting policy described in Theorem 11.10.2, how many trees are removed from the forest during each harvest?

Q:

- Describe at least three ways a for-profit healthcare firm can increase equity . Include brief examples of each. Use the following information to answer questions 3, 4, and 5: 2- You have been asked...

Q:

Balance sheet preparation Use the appropriate items from the following list to prepare in good form Mellarks Baked Goods balance sheet at December 31, 2015. Value ($000) at Value ($000) at Item...

Q:

b b. calculate the NPV and decide if the system is worth noting the date of retum month Indicated by a minus sign. Do not round Intermediate calculations. Round your new 2 Net procent value Worth...