Matrices Basic Operations

Front

What is a matrix?

Back

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

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns', indicating how many rows and columns it has.

Front

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

Back

Yes, you can multiply a 2x3 matrix by a 3x2 matrix because the number of columns in the first matrix matches the number of rows in the second.

Front

What is the result of multiplying a 2x3 matrix by a 3x2 matrix?

Back

The result 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

The product AB = [[58, 64], [139, 154]].

Front

What does it mean if two matrices cannot be multiplied?

Back

It means that the number of columns in the first matrix does not match the number of rows in the second 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 zero matrix?

Back

The zero matrix is a matrix in which all elements are zero.

Front

How do you find the transpose of a matrix?

Back

The transpose of a matrix is found by swapping its rows and columns.

Front

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

Back

The determinant is calculated as ad - bc.