Why we need to learn to find the inverse matrix of a matrix?

Why we need to learn to find the inverse matrix of a matrix?

just need three equations so i can create the matrices and i can solve from there.

Assume that producing 1 unit of coal requires 0.4 units of coal, 0.1 units of lumber, and 0.2 units of steel; that producing 1 unit of lumber requires 0 units of coal, 0.7 units of lumber, and 0.2...

[1 -1 1] [0 -1 0] [0 0 2] (the brackets are all suppose to be combined) Answer: first row=? second row=? third row=?

If A and B are any matrices of order 2×1, why does the product ABt have no inverse?

I tried to find the inverse but in all my multiplying, it ended up not being a inverse matrix and instead a random set of fractions in my matrix.

I need help with finding the inverse of the matrix for, -9 5 6 -3 I...

Production- Pretzels cost $4 per lb., dried fruit cost $5 per lb., and nuts cost $9 per lb. The three ingredients are to be combined in a trail mix containing twice the weight of pretzels as dried...