prove the following statement: If the augmented matrices of two linear systems are row equivalent, then...

prove the following statement: If the augmented matrices of two linear systems are row equivalent, then those systems are equivalent.

(To do this, start with a solution to one of the systems and show that it is still a solution of the other system under each of the three elementary row operations.)

Expert Solution

Colby Messinger answered 1 year ago

please give examples of four row equivalent matrices which are all in row echelon forms (not...

please give examples of four row equivalent matrices which are all in row echelon forms (not necessarly reduced row echelon)

1---- . Is the statement "Elementary row operations on an augmented matrix never change the solution...

1---- . Is the statement "Elementary row operations on an augmented matrix never change the solution set of the associated linear system" true or false? Explain. A. True, because elementary row operations are always applied to an augmented matrix after the solution has been found. B. False, because the elementary row operations make a system inconsistent. C. True, because the elementary row operations replace a system with an equivalent system. D. False, because the elementary row operations augment the number...

Write the following matrices into row echelon form.

Exercise1. Write the following matrices into row echelon form.

Exercise1. Write the following matrices into row echelon form. (a) A=⎛⎜⎝1132−22100474⎞⎟⎠A=(1132−22100474) (c) C=⎛⎜⎝121457210121331578⎞⎟⎠C=(121457210121331578) (b) B=⎛⎜⎝234304131⎞⎟⎠B=(234304131) (d) D=⎛⎜ ⎜ ⎜⎝11111−11−1−1−111−11λλ⎞⎟ ⎟ ⎟⎠

Suppose R and R0 are 2 ⇥ 3 row-reduced echelon matrices and that the systems RX...

Suppose R and R0 are 2 ⇥ 3 row-reduced echelon matrices and that the systems RX = 0 and R’X = 0 have exactly the same solutions. Prove that R = R’ .

The following matrix is the augmented matrix for a system of linear equations. A = 1...

The following matrix is the augmented matrix for a system of linear equations. A = 1 1 0 1 1 0 0 1 3 3 0 0 0 1 1 2 2 0 5 5 (a) Write down the linear system of equations whose augmented matrix is A. (b) Find the reduced echelon form of A. (c) In the reduced echelon form of A, mark the pivot positions. (d) Does the system have no solutions, exactly one solution or infinitely...

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prove the following statement: If the augmented matrices of two linear systems are row equivalent, then...

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