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Question : Solve the matrix equation for X : 2151852

**Solve the matrix equation for X.**

21)

Let A = and B = ;X + A = B

A)

X =

B)

X =

C)

X =

D)

X =

22)

Let A = and B =;X - B = A

A)

B)

C)

D)

23)

Let A = and B = ;4X + A = B

A)

X =

B)

X =

C)

X =

D)

X =

24)

Let A = and B = ;B - X = 3A

A)

X =

B)

X =

C)

X =

D)

X =

25)

Let A = and B = ;2B - 2A = X

A)

X =

B)

X =

C)

X =

D)

X =

**Find the product AB, if possible.**

26)

A = , B =

A)

B)

C)

D)

27)

A = , B =

A)

B)

C)

D) AB is not defined.

28)

A = , B =

A)

B)

C)

D) AB is not defined.

29)

A = , B =

A)

B)

C) AB is not defined.

D)

30)

A = , B =

A)

B)

C)

D)

31)

A = , B =

A)

B) AB is not defined.

C)

D)

32)

A = [-3 -1 6], B =

A)

B)

C)

D)

33)

A = , B =

A)

B)

C)

D)

34)

A = , B =

A)

B) AB is not defined.

C)

D)

35)

A = , B =

A)

B) AB is not defined.

C)

D)

**The ⊥ shape in the figure below is shown using 9 pixels in a 3 × 3 grid. The color levels are given to the right of the figure. Use the matrix **** that represents a digital photograph of the ⊥ shape to solve the problem.**

36) Adjust the contrast by changing the black to dark grey and the light grey to white. Use matrix addition to accomplish this.

A)

+ =

B)

+ =

C)

+ =

D)

+ =

37) Adjust the contrast by changing the black to light grey and the light grey to black. Use matrix addition to accomplish this.

A)

+ =

B)

+ =

C)

+ =

D)

+ =

38) Adjust the contrast by changing the black to white and the light grey to dark grey. Use matrix addition to accomplish this.

A)

+ =

B)

+ =

C)

+ =

D)

+ =

39) Adjust the contrast by leaving the black alone and changing the light grey to dark grey. Use matrix addition to accomplish this.

A)

+ =

B)

+ =

C)

+ =

D)

+ =

40) Using the same color levels from the instructions, write a 3 × 3 matrix A that represents the letter **L** in dark grey on a white background. Then find a 3 × 3 matrix B so that A + B lightens only the letter **L** from dark grey to light grey.

A)

A = ; B =

B)

A = ; B =

C)

A = ; B =

D)

A = ; B =

**Solve the problem using matrices.**

41) State University has a College of Arts & Sciences, a College of Business, and a College of Engineering. The percentage of students in each category are given by the following matrix.

The student population is distributed by class and age as given in the following matrix.

How many female students are in the College of Business? How many male students are in the College of Arts & Sciences?

A) 633 students; 1437 students

B) 531 students; 700 students

C) 1336 students; 633 students

D) 700 students; 523 students

42) The final grade for an algebra course is determined by grades on the midterm and final exam. The grades for four students and two possible grading systems are modeled by the following matrices.

Find the final course score for Student 3 for both grading System 1 and System 2.

A) System 1: 48.6; System 2: 53

B) System 1: 73.5; System 2: 88.5

C) System 1: 76.6; System 2: 76

D) System 1: 82.2; System 2: 81