Adding, subtracting and multiplying matrices Flashcard

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'.

Front

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. Add corresponding elements from each matrix.

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 matrix multiplication?

Back

Matrix multiplication involves taking the dot product of rows and columns from two matrices. The number of columns in the first matrix must equal the number of rows in the second.

Front

Can you multiply a 2x3 matrix by a 3x2 matrix?

Back

Yes, the resulting matrix will be a 2x2 matrix.

Front

What is the product of the matrices A = [[1, 2, 3], [4, 5, 6]] and B = [[7, 8], [9, 10], [11, 12]]?

Back

A * B = [[1*7 + 2*9 + 3*11, 1*8 + 2*10 + 3*12], [4*7 + 5*9 + 6*11, 4*8 + 5*10 + 6*12]] = [[58, 64], [139, 154]]

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 happens if you try to add matrices of different dimensions?

Back

You cannot add matrices of different dimensions; the operation is undefined.

Front

What is the zero matrix?

Back

The zero matrix is a matrix in which all elements are zero. It acts as the additive identity in matrix addition.

Front

How do you determine if two matrices can be multiplied?

Back

Two matrices can be multiplied if the number of columns in the first matrix equals the number of rows in the second matrix.