Pre-Calc Chapter 9

Front

What is a determinant in a matrix?

Back

A determinant is a scalar value that is a function of the entries of a square matrix. It provides important information about the matrix, such as whether it is invertible.

Front

How do you calculate the determinant of a 2x2 matrix?

Back

For a 2x2 matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the determinant is calculated as \( ad - bc \).

Front

What does it mean if the determinant of a matrix is zero?

Back

If the determinant of a matrix is zero, it means that the matrix is singular and does not have an inverse.

Front

What is an inverse matrix?

Back

An inverse matrix \( A^{-1} \) is a matrix that, when multiplied by the original matrix \( A \), yields the identity matrix \( I \).

Front

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

Back

For a 2x2 matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the inverse is given by \( \frac{1}{ad-bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \), provided that \( ad-bc \neq 0 \).

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

Solve the system of equations using elimination: 4x + 2y = 12 and 4x + 8y = -24.

Back

The solution is (6, -6).

Front

What is the relationship between a matrix and its determinant?

Back

The determinant provides information about the matrix's properties, such as whether it is invertible and the volume scaling factor of the linear transformation represented by the matrix.

Front

What is a singular matrix?

Back

A singular matrix is a square matrix that does not have an inverse, which occurs when its determinant is zero.

Front

How can you determine if a matrix is invertible?

Back

A matrix is invertible if its determinant is non-zero.