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Determinants, Adjoint & Inverse · Question 4 of 87

Question 4

EasyOriginal question

What is ∣x+2x−1x+1x∣\begin{vmatrix} x + 2 & x - 1 \\ x + 1 & x \end{vmatrix}?

Options for question 4

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. (x+2)x−(x−1)(x+1)=x2+2x−(x2−1)(x + 2)x - (x - 1)(x + 1) = x^2 + 2x - (x^2 - 1).

  2. =2x+1= 2x + 1.

Worth noting

2x−12x - 1 subtracts x2−1x^2 - 1 without the brackets, so its −1-1 keeps the wrong sign.

Concept
A determinant with algebraic entries
Typical time
60 s
Your time
—
The rule this testsThe determinant of a matrix
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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.