Computing Determinants of 2×2 or 3×3 Matrices
Read this topicExplanations 2
- (Video) Inverse of a 3×33\times33×3 Matrix by Math Meeting Here's a video by Math Meeting showing you how to find the inverse of a 3×33\times33×3 matrix using the determinant. I…
By Alex Federspiel, Anusha Rahman
- Butterfly Method / Sarrus' Rule I'm going to share with you a fun way to find the determinant of a 3×33\times33×3 matrix. My professor taught this to me and she called it the Bu…
By Alex Federspiel, Dave Tan
Problems 11
- A=[4325]A = \begin{bmatrix} 4 & 3 \\ 2 & 5 \end{bmatrix}A=[4235] What is det(A)\det(A)det(A)?
- A=[13−24210−37]A = \begin{bmatrix} 1 & 3 & -2 \\ 4 & 2 & 1 \\ 0 & -3 & 7 \end{bmatrix}A=14032−3−217 What is det(A)\det(A)det(A)?
- A=[243x]A = \begin{bmatrix} 2 & 4 \\ 3 & x \end{bmatrix}A=[234x] If det(A)=2\det(A) = 2det(A)=2, what is xxx?
- A=[145−2x0−163]A = \begin{bmatrix} 1 & 4 & 5 \\ -2 & x & 0 \\ -1 & 6 & 3 \end{bmatrix}A=1−2−14x6503 If det(A)=4\det(A) = 4det(A)=4, what is xxx?
- ∣7453∣=\begin{vmatrix} 7 & 4 \\ 5 & 3 \end{vmatrix} =7543=
- ∣523x∣=∣x8−13∣\begin{vmatrix} 5 & 2 \\ 3 & x \end{vmatrix} = \begin{vmatrix} x & 8 \\ -1 & 3 \end{vmatrix}532x=x−183 Find xxx.
- ∣x2241∣=∣1−1−2x∣≠1\begin{vmatrix} x^2 & 2 \\ 4 & 1 \end{vmatrix} = \begin{vmatrix} 1 & -1 \\ -2 & x \end{vmatrix} \neq 1x2421=1−2−1x=1 Find xxx.
- A=[2⋅det(A)−2det(A)+52]A = \begin{bmatrix} 2 \cdot\det(A) & -2 \\ \det(A) + 5 & 2 \end{bmatrix}A=[2⋅det(A)det(A)+5−22] What is det(A)\det(A)det(A)?
- What is the determinant of [−4−7−7−3−3−90−91]\begin{bmatrix}-4&-7&-7\\-3&-3&-9\\0&-9&1\end{bmatrix}−4−30−7−3−9−7−91?
- A=[336x22x15]A=\begin{bmatrix}3&3&6\\x&2&2\\x&1&5\end{bmatrix}A=3xx321625 and det(A)=42\det(A)=42det(A)=42. Find xxx.
- What is the determinant of [2abca2bcab2c]\begin{bmatrix}2a&b&c\\a&2b&c\\a&b&2c\end{bmatrix}2aaab2bbcc2c?