Matrices

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 matrix with 3 rows and 2 columns is said to have dimensions 3 x 2.

Front

What is a scalar in matrix multiplication?

Back

A scalar is a single number that can multiply each element of a matrix. For example, if you multiply a matrix by 3, each element of the matrix is multiplied by 3.

Front

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. You add corresponding elements together. For example, if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A + B = [[6, 8], [10, 12]].

Front

What is matrix subtraction?

Back

Matrix subtraction is similar to addition. You subtract corresponding elements of two matrices of the same dimensions. For example, if A = [[5, 6], [7, 8]] and B = [[1, 2], [3, 4]], then A - B = [[4, 4], [4, 4]].

Front

What is a scalar matrix?

Back

A scalar matrix is a square matrix in which all the elements are equal to the same scalar value. For example, [[3, 0], [0, 3]] is a scalar matrix where the scalar is 3.

Front

What does it mean for matrices to be compatible for addition?

Back

Matrices are compatible for addition if they have the same dimensions, meaning they have the same number of rows and columns.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. For example, the 2x2 identity matrix is [[1, 0], [0, 1]].

Front

How do you find the transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal. For example, if A = [[1, 2], [3, 4]], then the transpose A^T = [[1, 3], [2, 4]].

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero. For example, a 2x2 zero matrix is [[0, 0], [0, 0]].

Front

What is the determinant of a 2x2 matrix?

Back

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