Practice question · Multiple choice
There is a formula for the inverse of a 2×2 matrix and for 3×3, and nobody uses the general formula for a 10×10. Why does the explicit formula stop being useful so quickly?
Hints
- Count the terms in a cofactor expansion for n = 10. Compare with n³.
- Both routes give the right answer. Ask what separates them.
Show the answer
D. Because the cofactor expansion has n! terms, over three million at 10×10
Why
n! against n³ is the whole story: 3.6 million terms versus a few hundred operations, and by n = 20 the formula is beyond any computer while elimination is instant. The formula is a proof that the inverse exists and a description of it, it was never an instruction for computing one.
Practise Matrix Inverses
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