Back to Use matrix inverses to solve systems — Problem 2 · Task Set 47

HSA.REI.C.9 Tutor Intake — Matrix Inverses

This short check helps your tutor understand where to start. Answer each question without help. If you are not sure, give your best try — the goal is to find what to work on together, not to grade you.

Grade 9·8 problems·~13 min·Common Core Math - HS Algebra·standard·hsa-rei-c-9

Work through problems with immediate feedback

Concepts

A student wants to solve $Ax = b$ using the matrix inverse.
They write: $x = bA^{-1}$ .

What is wrong with this?

Nothing — $bA^{-1}$ and $A^{-1}b$ are equal because matrix
multiplication is commutative.

Matrix multiplication is not commutative. The correct order is
$x = A^{-1}b$ (multiply $A^{-1}$ on the LEFT of $b$ ).

The student should use $x = A^{-1} / b$ instead.

The student should multiply on the right: $x = bA$ (not $bA^{-1}$ ).