Matrix Operations

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'rows x columns'. For example, a matrix with 3 rows and 2 columns is said to have dimensions 3x2.

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimensions. For example, if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A + B = [[6, 8], [10, 12]].

Front

How do you simplify a matrix expression?

Back

To simplify a matrix expression, perform operations such as addition, subtraction, or scalar multiplication step by step, ensuring to follow the order of operations and matrix rules.

Front

What is scalar multiplication in matrices?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number). For example, if k = 2 and A = [[1, 2], [3, 4]], then kA = [[2, 4], [6, 8]].

Front

What is the result of adding two matrices of different dimensions?

Back

Adding two matrices of different dimensions is undefined. Both matrices must have the same dimensions to perform addition.

Front

What is the formula for matrix subtraction?

Back

Matrix subtraction is performed by subtracting corresponding elements of two matrices of the same dimensions. If A = [[a, b], [c, d]] and B = [[e, f], [g, h]], then A - B = [[a-e, b-f], [c-g, d-h]].

Front

What does it mean to calculate 2C - 5A for matrices A and C?

Back

Calculating 2C - 5A means to multiply each element of matrix C by 2, multiply each element of matrix A by 5, and then subtract the resulting matrix from the first.

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, meaning A * I = A for any matrix A.

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal, turning rows into columns and vice versa. If A = [[1, 2], [3, 4]], then A^T = [[1, 3], [2, 4]].

Front

What is the determinant of a 2x2 matrix?

Back

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