Solving Linear Systems with Matrices

What is the algebraic method of elimination also known as?

• Substitution

• Division

• Addition and Subtraction

• Multiplication

What does an augmented matrix represent?

• A polynomial equation

• A system of linear equations

• A single linear equation

• A quadratic equation

Which of the following is NOT an elementary row operation?

• Subtracting one row from another

• Adding one row to another

• Multiplying a row by a non-zero constant

• Dividing a row by zero

In the first example, what is the purpose of changing certain numbers to zeros using row operations?

• To find the determinant

• To transpose the matrix

• To solve for the variables

• To simplify the matrix

What is the purpose of back substitution in solving a system of equations?

• To solve for the variables

• To transpose the matrix

• To simplify the matrix

• To find the determinant

What is the result of having a whole row of zeros in a matrix?

• A single point of intersection

• A unique solution

• No solution

• An infinite number of solutions

In the second example, what does the parametric equation represent?

• A plane

• A unique point

• A circle

• A line of intersection

What does reduced row echelon form indicate about a matrix?

• It is not solvable

• It has infinite solutions

• It has a unique solution

• It has no solutions

In the final example, what does a row of zeros except the last number being non-zero imply?

• An infinite number of solutions

• No solution

• A unique solution

• A dependent system

What is the main diagonal in a matrix?

• The column with the highest values

• The diagonal from the top right to the bottom left

• The row with the highest values

• The diagonal from the top left to the bottom right