What Is a Matrix Inverse?
Read this topicExplanations 6
- From the word inverse itself, we can infer that it means undo an action. For example if you multiply aaa to bbb, then to "undo" this you want to multiply 1a\frac{1}{a}a1 to the…
By Samara Ren, Alex Federspiel
- (Video) Inverse Matrix Using Gauss-Jordan and Row Reduction by PatrickJMT Here are some videos by patrickJMT showing you a different method of finding the inverse of a matrix. N…
By Alex Federspiel
- (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
- (Video) Inverse Matrices, Column Space, and Null Space by 3Blue1Brown What is an inverse? While formulas and calculations are important, so is intuition. Below is a video that p…
By Heather, Alex Federspiel
- Inverse In general, the mathematical definition of an inverse is a reciprocal of a value. For example, the inverse (or reciprocal) of 444 is 14\frac1441. We can denote the inve…
By Anusha Rahman
- Matrix Inverse Before finding a matrix inverse, it’s important to understand basic matrix operations like adding and subtracting matrices. Also make sure you have reviewed zero …
By Anusha Rahman
Problems 13
- A=[2513]A = \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}A=[2153] What is A−1A^{-1}A−1?
- A=[42−1205−120]A = \begin{bmatrix} 4 & 2 & -1 \\ 2 & 0 & 5 \\ -1 & 2 & 0 \end{bmatrix}A=42−1202−150 What is the sum of all the terms in A−1A^{-1}A−1? Give your answer as a …
- A=[3−14−42−68−19]A = \begin{bmatrix} 3 & -1 & 4 \\ -4 & 2 & -6 \\ 8 & -1 & 9 \end{bmatrix}A=3−48−12−14−69 What is A−1A^{-1}A−1?
- Let AAA be a matrix. Which of the following statements are true? (Assume the dimensions match up for all addition and multiplication.)
- Let AAA and BBB be invertible matrices. Which of the following are always true?
- A matrix AAA is diagonalizable if there exist SSS and Λ\LambdaΛ such that Λ\LambdaΛ is diagonal (i.e. all entries not on the diagonal are zero) and A=SΛS−1A = S \Lambda S^{-1}A=…
- What is I−1I^{-1}I−1? (III refers to the identity matrix, with 1's on the diagonal and 0's everywhere else.)
- True or False\text{True or False}True or False === All matrices have an inverse.
- True or False\text{True or False}True or False === The zero matrix has an inverse.
- What is the inverse of [4−384]\begin{bmatrix}4&-3\\8&4\end{bmatrix}[48−34]?
- What is the inverse of [123014560]\begin{bmatrix}1&2&3\\0&1&4\\5&6&0\end{bmatrix}105216340?
- Find the inverse of [xyzx]\begin{bmatrix}x&y\\z&x\end{bmatrix}[xzyx].
- What is the inverse of [8675105468]\begin{bmatrix}8&6&7\\5&10&5\\4&6&8\end{bmatrix}8546106758?