Operations with Matrices

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form of rows x columns, indicating the number of rows and the number of columns in the matrix.

Front

Can you multiply a 2x3 matrix by a 3x12 matrix?

Back

Yes, you can multiply a 2x3 matrix by a 3x12 matrix because the number of columns in the first matrix (3) matches the number of rows in the second matrix (3).

Front

What is the result of multiplying a 2x3 matrix by a 3x12 matrix?

Back

The result will be a 2x12 matrix.

Front

What is the product of the following matrices: [[1, 2, 3], [4, 5, 6]] and [[7], [8], [9]]?

Back

The product is [[ 50], [122]].

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 is the zero matrix?

Back

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

Front

How do you find the transpose of a matrix?

Back

To find the transpose of a matrix, switch its rows and columns. The element at position (i, j) in the original matrix becomes the element at position (j, i) in the transposed matrix.

Front

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

Back

The determinant is calculated as ad - bc.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that when A is multiplied by A^-1, the result is the identity matrix.

Front

What conditions must a matrix meet to be invertible?

Back

A matrix must be square and have a non-zero determinant to be invertible.