MATHEMATICS II

and the detreminant of this matrix is

The other matrices we use in the Cramer’s rule are

and their determinats are

Then the solution is

   and as follows:

Now we add the equations to eliminate the term

 then one gets

If we back-subsitute

into the equations

we obtain

Then these lines intersect at the point

is

the inverse of

is

one has

then

is obtained.  Since

is given, we  should have

From this equation one has

Then answer is  

The other matrices we use in the Cramer’s rule are

The determinant of these matrices are

Hence the solution of this system of linear equations is

the point

must also provide both  of the equations. Hence we obtain

Then one gets

we obtain

Hence

consists of four rows and two columns.

 Correct answer is  E .

to have different signs. Hence the linear equations become

Now we add the equations to eliminate the term

 then one has 

into the equation

we obtain 

The solution is the ordered pair

Correct answer is C.

Is

Then determinant of the matrix

Correct answer is B.

is

The inverse of the matrix

is

Correct answer is  A .

Then we write

Since

is given from the equation

Correct answer is  D .

satisfies only the equations

while this pair  does not satisfy the equations of the remaining systems simultaneously.

Correct answer is  E .

lies on both lines

the equations

Must be satisfied then, on has 

 Correct answer is  C.

is evaluated from the Sarrus’ rule as  

Correct answer is  B

The solution of this system of linear equations is

Correct answer is  A

Correct answer is  D .

We find the determinant of the coefficient matrix using Sarrus’ rule:

and we find