MAT223 Readings 02

mat223_1_3.pdf

• Homogeneous System in Linear Algebra
• Linear Combination of Columns in Linear Algebra
• Basic Solutions to a System of Linear Equations
  mat223_2_1-2_3.pdf
• Ex:
  • $A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 2\\ 3& 4\\ 5& 6\end{array}\right]$
  • $A_{21}=4$
  • $A_{12}=2$
  • $B_{31}=5$
  • $B_{22}=4$
  • $A\ne B$ because they are not of the same size.
• Zero Matrix
• Identity Matrix
• Scaling and Adding Matrices
• Transposing and Symmetric Matrices
• Multiplying Matrices
• Ex:
  • $\begin{array}{ll}x+2y+3z& =4\\ 5x+6y+7z& =9\end{array}$ can be:
  • $A=\left[\begin{array}{ccc}1& 2& 3\\ 5& 6& 7\end{array}\right]$
  • $\overrightarrow{x}=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$
  • $\overrightarrow{b}=\left[\begin{array}{c}4\\ 9\end{array}\right]$
  • $A\overrightarrow{x}=\overrightarrow{b}$
  • $A\overrightarrow{x}=\left[\begin{array}{l}x+2y+3z\\ 5x+6y+7z\end{array}\right]$
  • $A\overrightarrow{x}=b=\left[\begin{array}{cc}x+2y+3z& 4\\ 5x+6y+7z& 9\end{array}\right]$
• Particular Solutions in Linear Algebra