Answers to the First 3 Matrix Assignments (Unless there are typographical errors)
1.) [10 -20 30]2.)
3.) Can’t be done4.)
5.) 6.)
7.) 8.)
9.) 10.)
11.) 12.)
13.) 14.)
15.) 16.)
17.) Can’t do…18.)
19.) 20.)
21.) Any matrix can be multiplied by a scalar.
22.) Matrices must have the same dimensions in order to be added.
23.) Add corresponding elements together. For example, add A2, 5 to B2, 5.
24.) The first matrix’s number of columns must equal the second matrix’s number of rows. For example: A (4 X 9) can be multiplied by a (9 X 12), because the 9’s “match”.
25.) To find the element in row m column n, multiply each element in row m of the first matrix by its corresponding element in column n of the second matrixand add the products together.
More Fun With Matrices
Number of columns … number of rows … row … column … nth…mth
No, the size of the matrix will change. An “m X n” matrix of zeros.
Multiply a matrix by -1 to obtain the additive inverse.
The matrix doesn’t change. They must be square in order to have a main diagonal and not to change the size of the original matrix.
1. 2. 3.
4. 5. 6.
7.8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20.
Can Matrices Be Even More Fun???
A) -6B) -10C) 6D) 5r + 12
A) -68B) 166
1. -152. 48
3. 8a + 124. 14 + 3x (-20 8x) = 14 + 3x + 20 + 8x = 11x + 34
5. k (0 + 8) = k 86. f(2) = 1 and f(5) = 10, so answer is 16.
7. 478. -85
9. 126 + (2) = 12810. 20b + 12
10. Let A = . Det(A) = ab ab = 0
11. Let A = . Det(2A) = det= 4ad 4bc.
4det(A) = 4(ad bc) = 4ad 4bc, so for any 2 X 2 matrix, det(2A) = 4det(A).
12. Let A = and let B = . Det(AB) = det =
(aw + by)(cx + dz) (cw + dy)(ax + bz) = acwx + adwz + bcxy + adwz + bdyz (acwx + bcwz + adxy + bdyz) = acwx + adwz + bcxy + bdyz acwx bcwz adxy bdyz =
adwz + bcxy bcwx adxy
Det(A)det(B) = (ad bc)(wz xy) = adwz adxy bcwz + bcxy, so they’re equal.
13. Let A = and let B = . Det(A+B) = det =
(a + w)(d + z) (c + y)(b + x) = ad + az + dw + wz (bc + cx + by + xy)
Det(A)+det(B) = (ad bc) + (wz xy), which doesn’t have as many terms, so they’re not equal.
14. x + 2y = 715. x + 2y 7 = 0 16. 8 7x = 2x + 21 9x = 13 so x = 13/9
Determinants of Larger Matrices
1. 3a 102. 4m 1
3. 524. 0
5. 126. 9
7. 28. 40
9. 4k2 + 10k 2410. 6x2 + 16