Midterm Review #1

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form of rows x columns. For example, a 3 x 2 matrix has 3 rows and 2 columns.

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 resulting matrix will have dimensions equal to the number of rows of the first matrix and the number of columns of the second matrix.

Front

What is the result of subtracting two matrices?

Back

The result of subtracting two matrices is a new matrix where each element is the difference of the corresponding elements from the two matrices.

Front

What is a determinant of 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 write a system of equations as an augmented matrix?

Back

An augmented matrix is formed by writing the coefficients of the variables in the system of equations in a matrix format, with an additional column for the constants.

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 when A is multiplied by A^-1, the result 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 of a matrix?

Back

A matrix is in row echelon form if all nonzero rows are above any rows of all zeros, and the leading coefficient of a nonzero row is always to the right of the leading coefficient of the previous row.

Front

What is a column vector?

Back

A column vector is a matrix with a single column and multiple rows, often used to represent a point or a direction in space.