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Determinants, Adjoint & Inverse · Question 70 of 87

Question 70

EasyOriginal question

How many solutions does the system 3x+y=43x + y = 4, x+2y=3x + 2y = 3 have?

Options for question 70

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. ∣A∣=5|A| = 5. It is not 0, so A−1A^{-1} exists and the solution is unique.

  2. (adj⁡A)B=[55](\operatorname{adj} A)B = \begin{bmatrix}5 \\ 5\end{bmatrix}.

Concept
A system with a unique solution
Typical time
60 s
Your time
—
The rule this testsConsistency of a system of equations
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Ten questions from Determinants, Adjoint & Inverse, at your own pace.

Practise this chapter →

Ten questions from Determinants, Adjoint & Inverse, at your own pace.