Practice question · Put in order
Order the steps of solving the system Ax = b using an inverse.
- Read off the solution as x = the inverse of A times b
- Compute the inverse of A using the 2 by 2 formula
- Simplify the left side to x, since the inverse of A times A is the identity
- Check that the determinant of A is nonzero
- Multiply both sides on the left by the inverse of A
Hints
- Establish that the inverse exists before trying to compute it.
- The inverse must be applied on the LEFT of both sides, because order matters.
Show the answer
- Check that the determinant of A is nonzero
- Compute the inverse of A using the 2 by 2 formula
- Multiply both sides on the left by the inverse of A
- Simplify the left side to x, since the inverse of A times A is the identity
- Read off the solution as x = the inverse of A times b
Why
Check invertibility, build the inverse, multiply on the left, simplify, read off x. Multiplying on the right would give A x A-inverse, which does not simplify, the side you multiply on is not a free choice for matrices.
Practise Matrix Inverses
The app has 4 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Matrix Inverses
- Consider the matrix with rows (1, 2) and (2, 4). Select every TRUE statement about it.
- Match each term to its meaning.
- The inverse of a product reverses the order: (AB)⁻¹ = B⁻¹A⁻¹, not A⁻¹B⁻¹. Why does undoing a composition…
- Sort each statement about inverses by whether it is true or false.
- There is a formula for the inverse of a 2×2 matrix and for 3×3, and nobody uses the general formula for a…