Part 4 | Test 6 | Time: 2 hours |
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- Solve the following system of equations using Matrices:

**Answer:**The solutions are:*x*=3,*y*=1,*z*=2. - Find the determinant of

**Answer:**The determinant is -28. - Find the inverse of the matrix

**Answer:**The inverse is - Find the area of the triangle formed by the vertices
, and (8,11).

**Answer:**The area is 7.5. - If , and
find the following:
- 3
*A*-4*B*

**Answer:** -

**Answer:** - .

**Answer:**

- 3
- Find all the solutions of the following system of linear equations:
**Answer:**The solutions are: . - If , find the following:
- Vertex.

**Answer:**The vertex is (4, -11). - Axis of Symmetry.

**Answer:**The axis of symmetry is*x*=4. - Minimum Value.

**Answer:**The minimum value is*y*=-11. - Maximum Value.

**Answer:**There is no maximum value. - Domain of
*f*(*x*).

**Answer:**The domain of*f*(*x*) is the set of all real numbers, or in interval notation, . - Range of
*f*(*x*).

**Answer:**The range of*f*(*x*) is the set of all .

- Vertex.
- When is

**Answer:**Both expressions are equal, when the domain is restricted to the interval . - Find a polynomial with zero of 7 of multiplicity 3, zero of -1 of
multiplicity of 4, zero of 0 with multiplicity 2, and zero of 1-i, of
multiplicity 3.

**Answer:**One such polynomial is - Find , if for .

**Answer:**. - Given the following constraints:
- Find the maximum value of
*z*=3*x*-5*y*.

**Answer:**The maximum value is 18 at*x*=6, and*y*=0. - Find the minimum value of
*x*=3*x*-5*y*.

**Answer:**The minimum value is 0 at*x*=0, and*y*=0.

- Find the maximum value of

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