MDETERM to test whether a system has one answer
A determinant of zero means the equations do not pin down a unique solution.
Task:
Each row of A2:C4 holds the coefficients of one equation in three unknowns. In B6 give the determinant, and in B7 show Unique solution when it is not zero and No unique solution when it is.
Hints
+5 XPno-hints bonusSolve it on your own to keep the bonus. Each hint gets one step closer to the formula.
Variations of MDETERM Function
0/2The same formula in the other shapes it takes at work.
The data in this exercise
This is the grid you start with. Cell references in the task — B6, C2 — point at the row numbers and column letters below.
| A | B | C | |
|---|---|---|---|
| 1 | x | y | z |
| 2 | 2 | 1 | 3 |
| 3 | 4 | -1 | 2 |
| 4 | 1 | 5 | 2 |
| 5 | |||
| 6 | Determinant | ||
| 7 | Verdict |
What this exercise teachesMay contain the answer
Before trying to solve a set of equations — with MINVERSE, say — the determinant tells you whether there is a single answer to find. A non-zero determinant means the three equations are independent; zero means at least one repeats information the others already carry.