Matrices (Operations & Determinants)

Front

What is the condition for multiplying two matrices?

Back

Matrices can be multiplied only if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Front

What is the result of multiplying a 2x3 matrix by a 3x4 matrix?

Back

The resulting matrix will have dimensions 2x4.

Front

What is the determinant of a 2x2 matrix?

Back

For a matrix [[a, b], [c, d]], the determinant is ad - bc.

Front

How do you find the difference of two matrices A and B?

Back

Subtract corresponding elements: (A-B)ij = Aij - Bij.

Front

What is the identity matrix?

Back

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

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal.

Front

What is the determinant of a 3x3 matrix?

Back

For a matrix [[a, b, c], [d, e, f], [g, h, i]], the determinant is a(ei - fh) - b(di - fg) + c(dh - eg).

Front

What does it mean for two matrices to be compatible for addition?

Back

Two matrices can be added if they have the same dimensions.

Front

What is the result of multiplying a matrix by a scalar?

Back

Each element of the matrix is multiplied by the scalar.

Front

What is the zero matrix?

Back

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