Matrix operations flashcards for linear algebra

Question 1

When is matrix addition $A+B$ defined?

Accepted Answer

Only when $A$ and $B$ have the same dimensions (both $m	imes n$). Then $(A+B)_{ij}=a_{ij}+b_{ij}$.

Question 2

State the entry formula for the product $AB$.

Accepted Answer

For $A$ ($m	imes n$) and $B$ ($n	imes p$), the $(i,j)$ entry is $$(AB)_{ij}=\sum_{k=1}^{n} a_{ik}b_{kj}.$$

Question 3

How do you find the inverse of a $2	imes2$ matrix, and when does it exist?

Accepted Answer

For $A=\begin{pmatrix}a&b\c&d\end{pmatrix}$, it exists iff $\det(A)=ad-bc
eq0$. Then $$A^{-1}=\frac{1}{ad-bc}\begin{pmatrix}d&-b\-c&a\end{pmatrix}.$$

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