Continuing Education Course #286Engineering Methods in Microsoft Excel

Part 1: Linear Algebra

1. An array isa. a list of data and the mathematical relationships used to describe itb. an ordered list or arrangement, of datac. a system of methods used to analyze a list of data

2. The dimensions of an array denotea. the amount of computer resources needed to manipulate the arrayb. the number of rows and columns used to arrange the elements of the arrayc. which functions can be performed on the elements of the array

Use the following arrays to answer Question 3 through Question 17.

3. A + B is equal toa.

b.

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c.

4. A - B is equal toa.

b.

c.

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5. 17*A is equal toa.

b.

c.

6. The transpose of B is equal to

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a.

b.

c.

7. Multiplying a scalar value of 22 by the transpose of A yieldsa.

b.

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c.

8. Two matrices can be multiplied ifa. the dimensions of the two matrices are the sameb. the outer dimension of the first matrix equals the inner dimension of the second matrixc. the inner dimensions of the two matrices are equal

9. The matrix multiplication of A*B yieldsa.

b.

c.

10. The matrix multiplication of B*B yieldsa.

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b.

c.

11. The matrix multiplication of A and the transpose of B yieldsa.

b.

c.

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12. The element-by-element multiplication of A .* B yieldsa.

b.

c.

13. The element-by-element multiplication of A .* A yieldsa.

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b.

c.

14. The determinant of A isa. 2793b. 273c. 23

15. The determinant of B isa. 86b. 886c. 1886

16. The inverse of the matrix A isa.

b.

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c.

17. The inverse of the matrix B isa.

b.

c.

18. The transpose of the matrix of cofactors is called thea. adjoint matrixb. inverse matrixc. matrix of minors

19. Which of the following is correcta. The adjoint of a matrix multiplied by the determinant of the matrix yields the inverse matrix.b. The transpose of a matrix multiplied by a scalar value of -1 yields the matrix of minors.

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c. The transpose of the matrix of cofactors multiplied by the identity matrix yields the inverse matrix.d. All of the abovee. None of the above

20. The 6x6 identity matrix isa.

b.

c.

Use the following to answer Question 21 and Question 22

Consider the following system of linear equations

4x4 = 53x3 = 4

5x1 + 6x2 + 7x3 + 8x4 = 9

4x2 + 3x3 + 2x4 = 1

21. The system of linear equations in matrix form is

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a.

b.

c.

22. The solution of the system of linear equations isa.

b.

c.

Use the following to answer Question 23 and Question 24

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Consider the following system of linear equations

2x1 - 7x2 + 3x3 + 5 x4 - 7x5 + 11x6 + 8x7 = 1145x1 + 7x2 - x3 + 9x4 - 6x5 + 3x6 - 5x7 = -11

13x1 + 11x2 + 8x3 + 7x4 + 4x5 + 2x6 + x7 = -2512x1 + x2 + 6x3 + 5x4 + 9x5 + 3x6 + 11x7 = -37

x1 - 4x2 + 7x3 - 3x4 + 9x5 - 2x6 + 6x7 = 4

4x1 + x2 - 6x3 - 3x4 + 8x5 - 7x6 - 4x7 = -91-7x1 - 2x2 + 5x3 + x4 + 9x5 + 3x6 - 4x7 = -50

23. The vector of right-hand-side terms isa.

b.

c. Either of the above.

24. The solution of the system of linear equations is

a. =

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b. =

c. =

25. Systems of equations with more than 8 unknowns and 8 equationsa. cannot be solved by matrix methodsb. can be solved by matrix methods but cannot be solved in Excelc. can be solved by matrix methods and can be rapidly solved in Excel

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