## Solve Linear Algebra exam

### April 9th, 2013 | Algebra | Comments Off

**Introduction to solve linear algebra for exam:**

The linear algebra is used to solve a process of the unknown quantity in which the equation is true. The linear algebra here is denoted as a two variable function with 14 inches/foot. There are one or more variables available to represent a plane and to solve equation. A simple linear function have one independent variable ( y = a + bx ) which is used to trace a straight line in graph.

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## Problem of linear algebra for exam:

A high school had 1300 students enrolled in 2004 and 1600 students in 2007. Conducting exam for students. If the student population P; when exam is conducted P grows as a linear function of time t, where t is the amount of years after 2004.

a) How many students will be enrolled in the school in 2009?

b) Solve a linear algebra function that relates to the student population to the time t.

**Solution:**

a) Consider the given information in pairs as (t , P). The year 2004 correspond to t = 0 and the year 2007 corresponds to t = 4, hence 2 ordered pairs

(0, 1300) and (4, 1600)

Since the population grows linearly with time t, we use two ordered pairs to find slope m for graph of P as follows

m = (1600 – 1300) / (7 – 4) = 100 students / year

If slope is m = 100 then the students population grows by 100 in every year. Solve the equation from 2004 to 2009 in 7 years then students population in 2009 will be

P(2009) = P(2004) + 8 * 100 = 1300 + 800 = 2100 students.

b) We know the slope and two points, use point slope form to find an equation for population P as a function of t as follows

P – P _{1} = m (t – t_{1})

P – 1300 = 100 (t – 0)

P = 100 t + 1300

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## Practice problem on linear algebra for exam:

A high school exam had 1100 students enrolled in 2005 and 1800 students in 2006. Conducting exam for students. If the student population P, when exam is conducted P grows as a linear function of time t, where t is the amount of years after 2005.

a) How many students will be enrolled in 2010?

b) Solve a linear algebra function that relates to student population to the time t.