No AI is used
  1. Beranda
  2. Kalkulator
  3. Kalkulator: Aljabar Linear
  4. Kalkulator Aljabar Linear

Determinan dari $$$\left[\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right]$$$

Kalkulator akan menghitung determinan dari matriks persegi $$$2$$$x$$$2$$$ $$$\left[\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right]$$$, dengan langkah-langkah yang ditampilkan.

Kalkulator terkait: Kalkulator Matriks Kofaktor

A

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Masukan Anda

Hitung $$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right|$$$.

Solusi

Determinan matriks 2x2 adalah $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right| = \left(2 \cos{\left(5 v \right)}\right)\cdot \left(10 \cos{\left(5 v \right)}\right) - \left(- 10 u \sin{\left(5 v \right)}\right)\cdot \left(0\right) = 20 \cos^{2}{\left(5 v \right)}$$$

Jawaban

$$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right| = 20 \cos^{2}{\left(5 v \right)}$$$A


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