Matrices and determinants

Question 1 of 10

Use Cramer's rule: x + y = 3, 2x − y = 0. Then x =

Question 2 of 10

The determinant of [[1, 0, 0], [0, 2, 0], [0, 0, 3]] is

Question 3 of 10

If det A = 4, then det(2A) for a 2 × 2 matrix A is

Question 4 of 10

Find the determinant of the 3 × 3 diagonal matrix with diagonal entries 1, 2 and 3.

Question 5 of 10

The inverse of [[2, 1], [1, 1]] is

Question 6 of 10

Find x if [[x, 2], [3, 4]] is singular.

Question 7 of 10

Find the determinant of [[1, 2, 3], [0, 1, 4], [5, 6, 0]].

Question 8 of 10

To solve the system AX = B when A is invertible, you calculate

Question 9 of 10

A matrix has no inverse if its determinant is

Question 10 of 10

Solve using matrices: 2x + y = 5, x + y = 3. Then x =