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Δβα\Delta _{\beta \alpha}
01
Linear equations
Δβα\Delta _{\beta \alpha}
02
Quadratic equations
Δβα\Delta _{\beta \alpha}
03
Functions
Δβα\Delta _{\beta \alpha}
04
Linear algebra
Δβα\Delta _{\beta \alpha}
04
Linear algebra
Starter
Attempt to solve this system using the Gaussian elimination you learned from chapter 1:
What linear algebra is involved in AA HL?
Generally, you'sll see matrix operations in AA HL when it comes to solving 3 equations in a system. Although this doesn'st sound like the linear algebra you expected when you first clicked on this chapter, I promise you, Gaussian elimination becomes interesting when involving more than 2 equations!
A deeper dive into Gaussian elimination
From Chapter 1, you know that there's different forms of an augmented matrix that lets you find solutions to systems involving 2 equations, and those rules almost exactly apply to systems with 3, despite having that 3rd row and an additional variable:
Note N04.0a - Reduced row form "forms"
1 solution:
(1□□□01□□001□)\begin{pmatrix} 1 & \square & \square & \square \\ 0 & 1 & \square & \square \\ 0 & 0 & 1 & \square \\ \end{pmatrix}
0 solutions:
(1□□□01□□000□)\begin{pmatrix} 1 & \square & \square & \square \\ 0 & 1 & \square & \square \\ 0 & 0 & 0 & \square \\ \end{pmatrix}
Infinite solutions:
(1□□□01□□0000)\begin{pmatrix} 1 & \square & \square & \square \\ 0 & 1 & \square & \square \\ 0 & 0 & 0 & 0 \\ \end{pmatrix}
Topics coming soon:
1) What happens when there's infinite solutions