Matrix Row Transformations Quiz

What is the primary method discussed for solving systems of linear equations?

• Graphical method

• Substitution method

• Matrix row transformations

• Trial and error

What does a coefficient matrix contain?

• The solutions to the equations

• The constants from the equations

• The coefficients of the variables

• The variables themselves

In an augmented matrix, what is added to the coefficient matrix?

• The inverse matrix

• The solution set

• The constant column

• The variable names

What is the purpose of transforming a matrix into reduced row echelon form?

• To easily read off the solutions

• To simplify the matrix

• To make the matrix larger

• To eliminate variables

What does the diagonal of ones in reduced row echelon form represent?

• The constant terms

• The identity matrix

• The coefficients of the variables

• The solutions to the system

Which of the following is NOT a basic row transformation?

• Multiplying a row by a nonzero number

• Adding a multiple of one row to another

• Multiplying a row by zero

• Interchanging two rows

How can you change the order of equations in a system without affecting the solution?

• By adding a constant to each equation

• By multiplying each equation by zero

• By interchanging the rows

• By removing a variable

What happens when you multiply a row by a nonzero number?

• The row becomes zero

• The solution changes

• The row is eliminated

• The row is scaled

What is the result of adding a multiple of one row to another?

• The matrix becomes larger

• The row being added to changes

• The row being added from changes

• The matrix becomes singular

Why is it important to avoid multiplying a row by zero?

• It makes the matrix unsolvable

• It changes the solution

• It eliminates the row

• It creates an identity matrix