Topics
1. Linear Equations and Functions
topic badge
AustraliaVIC
VCE 11 Methods 2023

1.10 Linear systems in 3 and 4 unknowns

Lesson
Worksheet
Practice
Worksheet
Systems of linear equations
1

Using a graphing calculator, find the inverse of the following matrices:

Round all entries to six decimal places.

a

A=\left[ \begin{matrix} \frac{4}{3} & 0.7 \\ 21 & \sqrt{2} \end{matrix}\right]

b

A=\left[ \begin{matrix} \sqrt{5} & 0.5 \\ -13 & \frac{1}{2} \end{matrix}\right]

c

A=\left[ \begin{matrix} \frac{2}{3} & \frac{4}{3} & -\frac{5}{3} \\ \frac{5}{3} & \frac{10}{3} & -\frac{14}{3} \\ -\frac{5}{3} & -\frac{17}{3} & \frac{25}{6} \end{matrix}\right]

d

A=\left[ \begin{matrix} 1.5 & 0.6 & 0.59 \\ 0.86 & 1.36 & 0.62 \\ 0.55 & 0.46 & 1.3 \end{matrix}\right]

2

Using a graphing calculator, solve the following system of equations by using the method of matrix inverses.

Give the solutions to six decimal places.

a
\begin{aligned} 2.7x + y &=\sqrt{2} \\ \sqrt{3}x- 3y &= 2 \end{aligned}
b
\begin{aligned} x - \sqrt{5}y &=2.3 \\ 0.79x+ y &= -8 \end{aligned}
3

Using a graphing calculator, solve the following system of equations by using the method of matrix inverses.

Give the solutions to six decimal places.

a
\begin{aligned} \left(\log 2\right)x + \left(\ln 7\right)y + \left(\ln 5\right)z &=9 \\ \left(\ln 7\right)x + \left(\log 2\right)y + \left(\ln 3\right)z &= 2 \\ \left(\log 19\right)x + \left(\ln 5\right)y +\left(\ln 3\right)z &= 5\end{aligned}
b
\begin{aligned} \sqrt{5}x + ey + \pi z &=2 \\ ex + \sqrt{5}y + \pi z &= 3 \\ \pi x + ey +\sqrt{5}z &= 1\end{aligned}
Sign up to access Worksheet
Get full access to our content with a Mathspace account
Book a Demo
Sign up for free

Outcomes

U1.AoS2.8

solution of a set of simultaneous linear equations (geometric interpretation only required for two variables) and equations of the form f(x) = g(x) numerically, graphically and algebraically.

U1.AoS2.19

set up and solve systems of simultaneous linear equations involving up to four unknowns, including by hand for a system of two equations in two unknowns

U1.AoS3.1

average and instantaneous rates of change in a variety of practical contexts and informal treatment of instantaneous rate of change as a limiting case of the average rate of change

What is Mathspace

About Mathspace