Matrix Operations

Front

What is matrix addition?

Back

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

Front

What must be true in order to ADD two matrices?

Back

The dimensions of the matrices must be equal. This means that both matrices must have the same number of rows and the same number of columns.

Front

What is the result of adding the matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

Back

A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]].

Front

What is the dimension of a matrix?

Back

The dimension of a matrix is defined by the number of rows and columns it contains, expressed as 'rows x columns'. For example, a matrix with 2 rows and 3 columns is said to have a dimension of 2x3.

Front

What is scalar multiplication of a matrix?

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*1, 2*2], [2*3, 2*4]] = [[2, 4], [6, 8]].

Front

What is the result of multiplying the matrix A = [[1, 2], [3, 4]] by the scalar k = 3?

Back

kA = [[3*1, 3*2], [3*3, 3*4]] = [[3, 6], [9, 12]].

Front

What is a square matrix?

Back

A square matrix is a matrix that has the same number of rows and columns. For example, a 2x2 matrix or a 3x3 matrix.

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

What is the determinant of a 2x2 matrix A = [[a, b], [c, d]]?

Back

The determinant of a 2x2 matrix is calculated as det(A) = ad - bc.

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix. The number of columns in the first matrix must equal the number of rows in the second matrix.