Question

Consider a system of linear equations with augmented matrix A and coefficient matrix C. In each...

  1. Consider a system of linear equations with augmented matrix A and coefficient matrix C. In each case

    either prove the statement or give an example showing that it is false.

    • If there is more than one solution, A has a row of zeros.
    • If A has a row of zeros, there is more than one solution.
    • If there is no solution, the row-echelon form of C has a row of zeros. • If the row-echelon form of C has a row of zeros there is no solution.

    Recall: The coefficient matrix C of a system of linear equations is the matrix obtained from the augmented matrix of the system by deleting its last column.

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

Homework Answers

Answer #1

NOTE: HI, IF YOU HAVE ANY DOUBTS AND QUERIES ON THIS ANSWER PLEASE FEEL FREE TO COMMENT BELOW. I WILL REPLY "ASAP" AND PLEASE DONT DISLIKE THIS ANSWER.
HOPE I ANSWERED YOUR QUESTION.
THANK YOU.........

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
Write the system of equations as an augmented matrix. Then solve the system by putting the...
Write the system of equations as an augmented matrix. Then solve the system by putting the matrix in reduced row echelon form. x+2y−z=-10 2x−3y+2z=2 x+y+3z=0
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.
Please give examples of matrices which (1) is an augmented matrix of a linear system which...
Please give examples of matrices which (1) is an augmented matrix of a linear system which 3 equations and 3 variables. (2) is an augmented matrix of a linear system which 3 equations and 3 variables and all variables should be presented. (3) is an augmented matrix of a linear system which 3 equations and 3 variables and one of the variables is not presented. (4) is an augmented matrix of a linear system which is inconsistent. (5) is an...
The augmented matrix below represents a system of linear equations associated with a real world prob-...
The augmented matrix below represents a system of linear equations associated with a real world prob- lem. The augmented matrix has already been completely row reduced. 1 0 6 12  0 1 −2 0  0000 (a) Use the reduced matrix to write down the parametric solution for the system as a point (x, y, z).    (b) Assuming that x, y, and z represent the number of whole items, determine how many “actual” solutions this system has, and...
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...
Solve the following system of linear equations: 3x2−9x3 = −3 x1−2x2+x3 = 2 x2−3x3 = 0...
Solve the following system of linear equations: 3x2−9x3 = −3 x1−2x2+x3 = 2 x2−3x3 = 0 If the system has no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system. If the system has infinitely many solutions, your answer may use expressions involving the parameters r, s, and t. You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix.
The augmented matrix represents a system of linear equations in the variables x and y. [1...
The augmented matrix represents a system of linear equations in the variables x and y. [1 0 5. ] [0 1 0 ] (a) How many solutions does the system have: one, none, or infinitely many? (b) If there is exactly one solution to the system, then give the solution. If there is no solution, explain why. If there are an infinite number of solutions, give two solutions to the system.
3) For the given system of equations: x+y-z=-6 x+2y+3z=-10 2x-y-13z=3 Rewrite the system as an augmented...
3) For the given system of equations: x+y-z=-6 x+2y+3z=-10 2x-y-13z=3 Rewrite the system as an augmented matrix. [4 pt] Find the reduced row echelon form of the matrix using your calculator, and write it in the spacebelow. [4 pt] State the solution(s) of the system of equations. [3 pt]
A system of linear equations is said to be homogeneous if the constants on the right-hand...
A system of linear equations is said to be homogeneous if the constants on the right-hand side are all zero. The system 2x1 − x2 + x3 + x4 = 0 5x1 + 2x2 − x3 − x4 = 0 −x1 + 3x2 + 2x3 + x4 = 0 is an example of a homogeneous system. Homogeneous systems always have at least one solution, namely the tuple consisting of all zeros: (0, 0, . . . , 0). This solution...
Let T be an linear transformation from ℝr to ℝs. Let A be the matrix associated...
Let T be an linear transformation from ℝr to ℝs. Let A be the matrix associated to T. Fill in the correct answer for each of the following situations (enter your answers as A, B, or C).   1. Every row in the row-echelon form of A has a leading entry.   2. Two rows in the row-echelon form of A do not have leading entries.   3. The row-echelon form of A has a leading entry in every column.   4. The row-echelon...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT