Linear Algebra Test

Linear function is a function with polynomial degree 1. This linear function matches a dependent variable with independent variable and maintains a relation in a simpler way. The linear algebra is the important method which is used in the linear function, variable function, linear equation, vector, matrix etc. This linear function is used in the high school and college students are using the linear function by using the linear algebra.

Sample Problem for linear algebra:


f is a linear function. Value of x and f(x) are given in the table below; complete the table using linear algebra

X                           f(x)

-1                          11

1                           –

–                           1

6                          -12

7                         --

–                          -35

Solution:

f is a linear function in linear algebra whose formula has the form to test is

f(x) = a x + b

where a and b are constants to be test and found. Note that 2 ordered pairs (-2,18) and (5,-19) are given in the table. These are two ordered pairs to test are used to write a system of linear equations as follows

11 = - 1 a + b and -12 = 6 a + b

Solve the above system to obtain a = - 3 and b = 2 and write the formula for function f as follows

f(x) = - 3 x + 2

We now use the formula for the f to find f(x) given x or find x given f(x).

for x = 0 , f(0) = -3(0) + 2 = 2

for f(x) = 1 , 1 = -3 x + 2 which gives x = 1/3

for x = 7 , f(7) = -3(7) + 2 = - 19

for f(x) = - 30 , -30 = -3 x + 2 which gives x = 32/3

We now put the values of the calculated above in the answer.

X                           f(x)

-1                          11

1                           2

1/3                         1

6                         -12

7                         -19

32/3                      -35


Practice problem:


Problem 1:
f is a linear function in linear algebra. Value of x and f(x) to test are given in the table below; complete the table.

X                              f(x)

-5                             15

1                               –

–                              1

10                         -14

8                             --

–                           -35


Problem 2:
f is a linear function. Value of x and f(x) to test are given in the table below; complete the table.

X                               f(x)

-6                             18

1                              –

–                             1

9                           -20

10                             --

–                             -40