Basics of Matrices

4 Activities

Suppose that A=[2−11103]A=\begin{bmatrix}
2&-1\\
1&1\\
0&3
\end{bmatrix}A=​210​−113​​ and B=[03−2−110]B=\begin{bmatrix}
0&3\\
-2&-1\\
1&0
\end{bmatrix}B=​0−21​3−10​​.

Find B−3AB-3AB−3A.

[2−1074−33]\begin{bmatrix}
2&-10\\7&4\\-3&3
\end{bmatrix}​27−3​−1043​​

[601219]\begin{bmatrix}
6&0\\1&2\\1&9
\end{bmatrix}​611​029​​

[−66−5−41−9]\begin{bmatrix}
-6&6\\-5&-4\\1&-9
\end{bmatrix}​−6−51​6−4−9​​

[28−5−233]\begin{bmatrix}
2&8\\-5&-2\\3&3
\end{bmatrix}​2−53​8−23​​

Not defined

I don't know

Practice: Matrix Operations

Given that A=[−123−4]A=\begin{bmatrix}
-1&2\\3&-4
\end{bmatrix}A=[−13​2−4​] and B=[11−22]B=\begin{bmatrix}1&1\\-2&2\end{bmatrix}B=[1−2​12​], let C=(3A−2BT+I2)TC=(3A-2B^T+I_2)^TC=(3A−2BT+I2​)T.  Determine C22C_{22}C22​.

Find x,y,zx,y,zx,y,z if 
[x1z2−13]+[2341y5]=[−3413−28].\begin{bmatrix}
x&1&z\\2&-1&3
\end{bmatrix}
+
\begin{bmatrix}
2&3&4\\
1&y&5
\end{bmatrix}
=
\begin{bmatrix}
-3&4&1\\
3&-2&8
\end{bmatrix}.[x2​1−1​z3​]+[21​3y​45​]=[−33​4−2​18​].
x=x=x= -5

Example: Matrix Operations

Example:
Given the matrices 𝐴=[100−3−22]𝐴=\begin{bmatrix}1&0\\0&-3\\-2&2\end{bmatrix}A=​10−2​0−32​​, B=[30201−2]\text{B}=\begin{bmatrix}3&0\\2&0\\1&-2\end{bmatrix}B=​321​00−2​​, and C=[12010−1]C=\begin{bmatrix}1&2&0\\1&0&-1\end{bmatrix}C=[11​20​0−1​],
a) Find 2A−B2A-B2A−B.

Matrix Basics

Given the matrix A=[201013002]A=\begin{bmatrix}
2&0&1\\0&1&3\\0&0&2
\end{bmatrix}A=​200​010​132​​,  define B=A+03×3−2I3B=A+0_{3\times3}-2I_3B=A+03×3​−2I3​ and find the following entries.

Basics of Matrices

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Basics of Matrices

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Practice: Matrix Operations

Example: Matrix Operations

Matrix Basics