Linear algebra-4

Algebra Level 1

find the determinant of the matrix det ⁡ ( a ) = ∣ 1 2 3 4 ∣ . \det(a)=\begin{vmatrix} 1&2\\3&4\end{vmatrix}.


The answer is -2.

Aareyan Manzoor by Aareyan Manzoor , 18, USA

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2 solutions

Aareyan Manzoor
May 20, 2017

the determinant for a two by two matrix is ∣ a b c d ∣ = a d − b c \begin{vmatrix} a&b\\c&d\end{vmatrix}=ad-bc using that d e t ( a ) = 1 ∗ 4 − 2 ∗ 3 = − 2 det(a)=1*4-2*3=\boxed{-2}

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Can you review the choice of brackets? Using ∣ ⋅ ∣ | \cdot | is often for just the determinant, and you're missing the matrix brackets.

Calvin Lin Staff - 4 years ago

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i know, since the questions asks for determinant i used those brackets. thats how i have seen the determinant written. am i suppose to add the regular brackets before the determinant brackets?

Aareyan Manzoor - 4 years ago

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Oh, I just looked up the notation and that is what it is. So no change needed.

Having the double brackets would seem weird

∣ ( 1 2 3 4 ) ∣ \left| \begin{pmatrix} 1&2\\3&4\end{pmatrix} \right|

Calvin Lin Staff - 4 years ago

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