Matrix Review

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

What is the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.

Front

How do you solve a system of equations using matrices?

Back

You can solve a system of equations by representing it in matrix form and using methods like substitution, elimination, or matrix inversion.

Front

What does M_ij represent in a matrix?

Back

M_ij represents the element located in the i-th row and j-th column of matrix M.

Front

What is the value of the determinant for a matrix with rows that are linearly dependent?

Back

The determinant of a matrix with linearly dependent rows is 0.

Front

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The element in the resulting matrix is the dot product of the corresponding row and column.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that AA^-1 = A^-1A = I, where I is the identity matrix.

Front

What is a scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number).

Front

What is a row echelon form?

Back

Row echelon form is a form of a matrix where all non-zero rows are above any rows of all zeros, and the leading coefficient of a non-zero row is always to the right of the leading coefficient of the previous row.