Question

Determine whether the following statements are true or false and provide a justification for your response....

Determine whether the following statements are true or false and provide a justification for your response.

  1. If the coefficient matrix of a system of linear equations has a pivot in the rightmost column, then the system is inconsistent.

  2. If a system of equations has two equations and four unknowns, then it must be consistent.

  3. If a system of equations having four equations and three unknowns is consistent, then the solution is unique.

  4. Suppose that a linear system has four equations and four unknowns and that the coefficient matrix has four pivots. Then the linear system is consistent and has a unique solution.

  5. Suppose that a linear system has five equations and three unknowns and that the coefficient matrix has a pivot in every column. Then the linear system is consistent and has a unique solution.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(6) Label each of the following statements as True or False. Provide justification for your response....
(6) Label each of the following statements as True or False. Provide justification for your response. (b) True/False The scalar λ is an eigenvalue of a square matrix A if and only if the equation (A − λIn)x = 0 has a nontrivial solution. (c) True/False If λ is an eigenvalue of a matrix A, then there is only one nonzero vector v with Av = λv. (d) True/False The eigenspace of an eigenvalue of an n × n matrix...
Is each statement true or false? If true, explain why; if false, give a counterexample. a)...
Is each statement true or false? If true, explain why; if false, give a counterexample. a) A linear system with 5 equations and 4 unknowns is always inconsistent. b) If the coefficient matrix of a homogeneous system has a column of zeroes, then the system has infinitely many solutions. (Note: a homogeneous system has augmented matrix [A | b] where b = 0.) c) If the RREF of a homogeneous system has a row of zeroes, then the system has...
True/ false a- If the last row in an REF of an augmented matrix is [0...
True/ false a- If the last row in an REF of an augmented matrix is [0 0 0 4 0], then the associated linear system is inconsistent. b-The equation Ax=b is consistent if the augmented matrix [A b] has a pivot position in every row. c-The set Span{v} for a nonzero v is always a line that may or may not pass through the origin.
For each statement below, either show that the statement is true or give an example showing...
For each statement below, either show that the statement is true or give an example showing that it is false. Assume throughout that A and B are square matrices, unless otherwise specified. (a) If AB = 0 and A ̸= 0, then B = 0. (b) If x is a vector of unknowns, b is a constant column vector, and Ax = b has no solution, then Ax = 0 has no solution. (c) If x is a vector of...
7. Answer the following questions true or false and provide an explanation. • If you think...
7. Answer the following questions true or false and provide an explanation. • If you think the statement is true, refer to a definition or theorem. • If false, give a counter-example to show that the statement is not true for all cases. (a) Let A be a 3 × 4 matrix. If A has a pivot on every row then the equation Ax = b has a unique solution for all b in R^3 . (b) If the augmented...
Establish whether the following statements are TRUE, FALSE, or AMBIGUOUS and provide a justification for your...
Establish whether the following statements are TRUE, FALSE, or AMBIGUOUS and provide a justification for your answer. In a perfect capital market, shareholders prefer not to use debt because equity becomes riskier as the debt-to-equity ratio increases?
true/false : if a system of linear equations has a 3x5 augmented matrix whose fifth column...
true/false : if a system of linear equations has a 3x5 augmented matrix whose fifth column has a leading term, then the system is consistent. I know the answer is false, but why? This is all the information provided in the question.
Determine whether the following statements are true or false. If the statement is false, then explain...
Determine whether the following statements are true or false. If the statement is false, then explain why the statement is false or rewrite the statement so that it is true. If a scatterplot shows a linear association between two numerical variables, then a correlation coefficient that is close to 1 indicates a strong positive trend and a correlation coefficient that is close to 0 indicates a strong negative trend.
Answer all of the questions true or false: 1. a) If one row in an echelon...
Answer all of the questions true or false: 1. a) If one row in an echelon form for an augmented matrix is [0 0 5 0 0] b) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. c) The solution set of b is the set of all vectors of the form u = + p + vh where vh is any solution...
QUESTION 4 Determine if each of the following statements is True or False with full justification...
QUESTION 4 Determine if each of the following statements is True or False with full justification explaining your reasoning. In multiple regression, a large R square indicates all independent variables will have a significant effect on the dependent variable if the significance level is set to 5%.                    (1 mark) In multiple regression, if an you have an independent variable with a large p-value (close to 1), this independent variable cannot be used to predict the dependent variable.     (1...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT