Front

What is a determinant in a matrix?

Back

The 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 is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimensions. For example, if A = \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) and B = \( \begin{pmatrix} e & f \\ g & h \end{pmatrix} \), then A + B = \( \begin{pmatrix} a+e & b+f \\ c+g & d+h \end{pmatrix} \).

Front

What does it mean for a matrix to be invertible?

Back

A matrix is invertible if there exists another matrix such that when multiplied together, they yield the identity matrix. This is only possible if the determinant of the matrix is non-zero.

Front

What is the absolute value function?

Back

The absolute value function, denoted as \( |x| \), returns the non-negative value of x. For example, \( |3| = 3 \) and \( |-3| = 3 \).

Front

How do you solve the equation \( |8+p|=2p-3 \)?

Back

To solve \( |8+p|=2p-3 \), consider two cases: 1) \( 8+p = 2p-3 \) and 2) \( 8+p = -(2p-3) \). Solving these gives p = 11.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation. This reduces the system to one equation with one variable.

Front

What is the solution to the system of equations: \( x + y = 5 \) and \( x - y = 1 \)?

Back

The solution is (3, 2). You can find this by solving the equations simultaneously.

Front

What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?

Back

The determinant is calculated as \( (1)(4) - (2)(3) = 4 - 6 = -2 \).