Assessment: Matrices

What does the "order" of a matrix describe?

A matrix has an inverse exactly when its determinant is:

Find A+B, where A=[[2,1],[0,3]] and B=[[1,4],[5,2]].

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

For A=[[1,3],[2,0]] and B=[[2,1],[4,5]], find the (2,2) entry of AB.

Find the inverse of [[1,0],[0,1]] (the identity matrix).

Why is the matrix method (X = A⁻¹B) especially useful for large systems of equations?

A quantities matrix (recipes × ingredients) is multiplied by a cost matrix (ingredients × 1) to get total recipe costs. What must be true for this multiplication to work?

Solve 3x + 2y = 16 and x + y = 7 using matrices. Find y. (A=[[3,2],[1,1]], det=1.)

A matrix [[2,4],[1,2]] is given. What happens when you try to find its inverse?