Linear Algebra final exam

Fifteen questions on all of Linear Algebra. Answer all 15 to see your score. Questions are drawn from a bank of 45, so every attempt is different.

0 of 15 answered

Question 1 of 15

The dot product of (1, 3, -2) and (4, -1, 1) is:

The length of (2, 3, 6) is:

Three vectors in R^3 are linearly dependent if:

A basis of a vector space must be:

The dimension of the space of 3 x 3 matrices is:

A consistent linear system with free variables has:

Reduced row echelon form requires every pivot to be:

The general solution of Ax = b is any particular solution plus:

If A is 2 x 4 and B is 4 x 3, the product AB is:

For square matrices, (AB)^{-1} equals:

The inverse of [[1, 2], [3, 7]] is:

In A = LU, solving Ax = b uses:

The determinant of [[2, 1, 0], [0, 3, 4], [0, 0, 5]] is:

Swapping two rows of a matrix with determinant 7 gives determinant:

If det A = 3 for a 2 x 2 matrix A, then det(4A) is: