Vectors and matrices — Question 5

QCAA 2021, Paper 1 · 1 mark

Q5 · 2021 · Technology-freeSimple familiar1 mark

QUESTION 5

The augmented matrix shown is produced when a Gaussian elimination technique is used to solve a certain system of equations with three variables.

\left[\begin{array}{ccc|c}1&1&-3&4\\0&-1&5&-6\\0&0&1&0\end{array}\right]

The geometric interpretation of the solution to this system of equations is best represented by

Four diagrams showing geometric arrangements of three planes.

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

Worked solution

There is a pivot in each of the three variable columns, so the system has one unique solution. Geometrically, the three planes therefore share exactly one common point, represented by option D.

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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