Solving Systems of Equations using Matrices (CFA)

Front

What happens when both equations in a system are the same line?

Back

You will have infinite solutions.

Front

What does it mean if the inverse of a matrix does not exist?

Back

The matrix is singular and cannot be inverted.

Front

What is the identity matrix?

Back

A square matrix with ones on the diagonal and zeros elsewhere.

Front

What is the equation used to solve a system AX=B using inverse matrices?

Back

X=A⁻¹B

Front

What does the graph of a system of equations with one solution look like?

Back

Intersecting lines.

Front

What is Cramer's Rule used for?

Back

To solve systems of linear equations using determinants.

Front

What is row echelon form?

Back

A form of a matrix where all non-zero rows are above any rows of all zeros, and leading coefficients of a non-zero row are to the right of the leading coefficients of the previous row.

Front

What is the determinant of a 2x2 matrix?

Back

For a matrix [[a, b], [c, d]], the determinant is ad - bc.

Front

How do you find the inverse of a 2x2 matrix?

Back

For a matrix [[a, b], [c, d]], the inverse is (1/det) * [[d, -b], [-c, a]], where det = ad - bc.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

They have no solutions because they never intersect.