Practice problem
Find the inverse of [xyzx]\begin{bmatrix}x&y\\z&x\end{bmatrix}[xzyx].
[xx2−yz−yx2−yz−zx2−yzxx2−yz]\begin{bmatrix}\dfrac{x}{x^2-yz}&-\dfrac{y}{x^2-yz}\\-\dfrac{z}{x^2-yz}&\dfrac{x}{x^2-yz}\end{bmatrix}x2−yzx−x2−yzz−x2−yzyx2−yzx
[xx2−yzyx2−yzzx2−yzxx2−yz]\begin{bmatrix}\dfrac{x}{x^2-yz}&\dfrac{y}{x^2-yz}\\\dfrac{z}{x^2-yz}&\dfrac{x}{x^2-yz}\end{bmatrix}x2−yzxx2−yzzx2−yzyx2−yzx
[x−y−zx]\begin{bmatrix}x&-y\\-z&x\end{bmatrix}[x−z−yx]
[x2x−yz−y2x−yz−z2x−yzx2x−yz]\begin{bmatrix}\dfrac{x}{2x-yz}&-\dfrac{y}{2x-yz}\\-\dfrac{z}{2x-yz}&\dfrac{x}{2x-yz}\end{bmatrix}2x−yzx−2x−yzz−2x−yzy2x−yzx
Type a concept, like “slope” or “photosynthesis”.
