Operations - Matrices

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimensions.

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 scalar multiplication of a matrix?

Back

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

Front

What is the result of multiplying the matrix B = [[2, 3], [4, 5]] by the scalar 3?

Back

3B = [[3*2, 3*3], [3*4, 3*5]] = [[6, 9], [12, 15]]

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix.

Front

What is the condition for two matrices to be multiplied?

Back

The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

If A is a 2x3 matrix and B is a 3x2 matrix, what is the size of the resulting matrix AB?

Back

The resulting matrix AB will be a 2x2 matrix.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

What is the result of multiplying any matrix by the identity matrix?

Back

Multiplying any matrix by the identity matrix of compatible size results in the original matrix.