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MATH1014 Quizzes

Quiz 7: Matrix Operations
Question 1 Questions
What is the size of the matrix A = 1 2 3412 3 4 1 131412  ? Exactly one option must be correct)
a)
2 × 3
b)
3 × 2
c)
3 × 4
d)
4 × 3

Choice (a) is incorrect
Try again. The size of a matrix is the number of rows × the number of columns.
Choice (b) is incorrect
Try again. The size of a matrix is the number of rows × the number of columns.
Choice (c) is correct!
A has 3 rows and 4 columns and hence it is a 3 × 4 matrix.
Choice (d) is incorrect
Try again. The size of a matrix is the number of rows × the number of columns.
What is the (2,3) entry in the matrix A = 1 2 3412 3 4 1 131412  ? Exactly one option must be correct)
a)
3
b)
4
c)
12
d)
14

Choice (a) is incorrect
Try again. The (2,3) entry is in row 2 and column 3.
Choice (b) is correct!
We are looking for the entry in the second row and the third column of A, which is 4.
Choice (c) is incorrect
Try again. The (2,3) entry is in row 2 and column 3.
Choice (d) is incorrect
Try again. The (2,3) entry is in row 2 and column 3.
Which sums can be made from the following matrices ?
A = 123 4 5 6 ,B = 12 5 6 ,C = 123 4 5 6 789 ,D = 12 3 4 .
(Zero or more options can be correct)
a)
A + A
 b)
A + B
 c)
A + C
d)
A + D
 e)
B + A
 f)
B + B
g)
B + D
 h)
C + A
 i)
C + C
j)
C + D
 k)
D + A
 l)
D + C
m)
D + D
 n)
D + B

There is at least one mistake.
For example, choice (a) should be True.
There is at least one mistake.
For example, choice (b) should be False.
Only matrices of the same size can be added.
There is at least one mistake.
For example, choice (c) should be False.
Only matrices of the same size can be added.
There is at least one mistake.
For example, choice (d) should be False.
Only matrices of the same size can be added.
There is at least one mistake.
For example, choice (e) should be False.
Only matrices of the same size can be added.
There is at least one mistake.
For example, choice (f) should be True.
There is at least one mistake.
For example, choice (g) should be True.
There is at least one mistake.
For example, choice (h) should be False.
Only matrices of the same size can be added.
There is at least one mistake.
For example, choice (i) should be True.
There is at least one mistake.
For example, choice (j) should be False.
Only matrices of the same size can be added.
There is at least one mistake.
For example, choice (k) should be False.
There is at least one mistake.
For example, choice (l) should be False.
Only matrices of the same size can be added.
There is at least one mistake.
For example, choice (m) should be True.
There is at least one mistake.
For example, choice (n) should be True.
Correct!
  1. True
  2. False Only matrices of the same size can be added.
  3. False Only matrices of the same size can be added.
  4. False Only matrices of the same size can be added.
  5. False Only matrices of the same size can be added.
  6. True
  7. True
  8. False Only matrices of the same size can be added.
  9. True
  10. False Only matrices of the same size can be added.
  11. False
  12. False Only matrices of the same size can be added.
  13. True
  14. True
Let A = 13 4 2 10 7 and B = 523 0 11 12 . What is A + B? Exactly one option must be correct)
a)
651 2 21 5
b)
13 4 523 2 10 7 0 11 12
c)
651 2 21 5
d)
13 4 2 10 7 523 5 2 3
e)
6 5 1 2 21 5
f)
A + B is undefined

Choice (a) is incorrect
Matrix addition is defined by adding the corresponding entries of the two matrices.
Choice (b) is incorrect
Matrix addition is defined by adding the corresponding entries of the two matrices.
Choice (c) is correct!
Choice (d) is incorrect
Matrix addition is defined by adding the corresponding entries of the two matrices.
Choice (e) is incorrect
Choice (f) is incorrect
Matrix addition is defined by adding the corresponding entries of the two matrices.
If A = 1 0 3 2 1 2 0 2 1 find the matrix 7A. Exactly one option must be correct)
a)
7 0 21 2 1 2 0 2 1
b)
1 0 3 14 7 14 0 2 1
c)
1 0 3 2 1 2 0147
d)
7 0 2114 7 14 0 14 7

Choice (a) is incorrect
When multiplying a matrix by a scalar, each entry in the matrix is multiplied by the scalar.
Choice (b) is incorrect
When multiplying a matrix by a scalar, each entry in the matrix is multiplied by the scalar.
Choice (c) is incorrect
When multiplying a matrix by a scalar, each entry in the matrix is multiplied by the scalar.
Choice (d) is correct!
Consider the four matrices
A = 123 4 5 6 ,B = 12 3 4 56 ,C = 123 4 5 6 789 andD = 12 3 4 .
Which of the following products can be made from these matrices ? (Zero or more options can be correct)
a)
AB
 b)
AC
 c)
AD
d)
A2
 e)
BA
 f)
BD
g)
B2
 h)
CA
 i)
CB
j)
CD
 k)
CB
 l)
C2
m)
DA
 n)
DC
 o)
CB
p)
D2

There is at least one mistake.
For example, choice (a) should be True.
A is a 2 × 3 matrix hence we can only post-multiply A by a matrix with 3 rows and pre-multiply A by a matrix with 2 columns.
There is at least one mistake.
For example, choice (b) should be True.
There is at least one mistake.
For example, choice (c) should be False.
A is a 2 × 3 matrix hence we can only post-multiply A by a matrix with 3 rows and pre-multiply A by a matrix with 2 columns.
There is at least one mistake.
For example, choice (d) should be False.
A is a 2 × 3 matrix hence we can only post-multiply A by a matrix with 3 rows and pre-multiply A by a matrix with 2 columns.
There is at least one mistake.
For example, choice (e) should be True.
There is at least one mistake.
For example, choice (f) should be True.
There is at least one mistake.
For example, choice (g) should be False.
B is a 3 × 2 matrix hence we can only post-multiply B by a matrix with 2 rows and pre-multiply B by a matrix with 3 columns.
There is at least one mistake.
For example, choice (h) should be False.
C is a 3 × 3 matrix hence we can only post-multiply C by a matrix with 3 rows and pre-multiply C by a matrix with 3 columns
There is at least one mistake.
For example, choice (i) should be True.
There is at least one mistake.
For example, choice (j) should be False.
C is a 3 × 3 matrix hence we can only post-multiply C by a matrix with 3 rows and pre-multiply C by a matrix with 3 columns
There is at least one mistake.
For example, choice (k) should be True.
There is at least one mistake.
For example, choice (l) should be True.
There is at least one mistake.
For example, choice (m) should be True.
There is at least one mistake.
For example, choice (n) should be False.
C is a 3 × 3 matrix hence we can only post-multiply C by a matrix with 3 rows and pre-multiply C by a matrix with 3 columns
There is at least one mistake.
For example, choice (o) should be True.
There is at least one mistake.
For example, choice (p) should be True.
Correct!
  1. True A is a 2 × 3 matrix hence we can only post-multiply A by a matrix with 3 rows and pre-multiply A by a matrix with 2 columns.
  2. True
  3. False A is a 2 × 3 matrix hence we can only post-multiply A by a matrix with 3 rows and pre-multiply A by a matrix with 2 columns.
  4. False A is a 2 × 3 matrix hence we can only post-multiply A by a matrix with 3 rows and pre-multiply A by a matrix with 2 columns.
  5. True
  6. True
  7. False B is a 3 × 2 matrix hence we can only post-multiply B by a matrix with 2 rows and pre-multiply B by a matrix with 3 columns.
  8. False C is a 3 × 3 matrix hence we can only post-multiply C by a matrix with 3 rows and pre-multiply C by a matrix with 3 columns
  9. True
  10. False C is a 3 × 3 matrix hence we can only post-multiply C by a matrix with 3 rows and pre-multiply C by a matrix with 3 columns
  11. True
  12. True
  13. True
  14. False C is a 3 × 3 matrix hence we can only post-multiply C by a matrix with 3 rows and pre-multiply C by a matrix with 3 columns
  15. True
  16. True
If A is a 2 × 3 matrix, and B is a 3 × 4 matrix, how many columns does AB have? (Enter your answer into the answer box.)

Correct!
AB is a 2 × 4 matrix, and so has 4 columns.
Incorrect. Please try again.
Remember that an n × m matrix, multiplied by an m × p matrix, is an n × p matrix.
Let A = 13 4 2 10 7 0 1 0 0 0 0 and B = 5 0 2 11 312 . Which of the following matrices is equal to the matrix AB? Exactly one option must be correct)
a)
115 11 26 312 0 0
b)
1 0 4 26 0 12 0 0
c)
115 11 26 211 0 0
d)
115 11 26 211 6 0
e)
AB is undefined

Choice (a) is incorrect
Since A is a 4 × 3 matrix and B is a 3 × 2 matrix the product AB is a 4 × 2 matrix.
Choice (b) is incorrect
The entry in row 1 and column 2 of AB is 15.
Choice (c) is correct!
Choice (d) is incorrect
The entry in row 4 and column 1 of AB is 0.
Choice (e) is incorrect
Since A is a 4 × 3 matrix and B is a 3 × 2 matrix the product AB is a 4 × 2 matrix. In particular, the product of A and B is defined.
Let
W = 123 3 2 1 ,X = 1 0 2 1 0 2 andY = 0 12 5
Which of the following statements are correct? (Zero or more options can be correct)
a)
WX +Y = 55 5 5
b)
XY = 0 1 2 3 410
c)
XW +Y = 25 3 0
d)
Y W = 32 1 13 6 1
e)
WXY = 820 8 13

There is at least one mistake.
For example, choice (a) should be True.
There is at least one mistake.
For example, choice (b) should be True.
There is at least one mistake.
For example, choice (c) should be False.
XW is a 3 × 3 matrix so the sum XW + Y is does not make sense because we can only add matrices of the same size.
There is at least one mistake.
For example, choice (d) should be True.
There is at least one mistake.
For example, choice (e) should be False.
WX = 54 7 0 so WXY = 825 0 7 .
Correct!
  1. True
  2. True
  3. False XW is a 3 × 3 matrix so the sum XW + Y is does not make sense because we can only add matrices of the same size.
  4. True
  5. False WX = 54 7 0 so WXY = 825 0 7 .
Let
W = 13 2 2 3 1 ,X = 3 2 11 2 3 2 11 ,Y = 1 2 0 0 1 2 andZ = 01 2 3 .
Which of the following statements are true ? (Zero or more options can be correct)
a)
WY X = 237 3 4 7 1 6 1
b)
Y W Z2 = 59 0 2
c)
The product (Y W)2 is not defined.
d)
(Y W)2 = Y 2W2
e)
Y W Z2 = 58 2 1
f)
WY X = 237 3 4 7 1 6 1 ,
g)
Y W Z2 = 3 102 7 .

There is at least one mistake.
For example, choice (a) should be True.
There is at least one mistake.
For example, choice (b) should be False.
Y W Z2 = 3 102 7 .
There is at least one mistake.
For example, choice (c) should be False.
Y W is a 2 × 2 matrix so its square is defined. In fact, (Y W)2 = 363 36 12
There is at least one mistake.
For example, choice (d) should be False.
If A is a matrix then A2 is defined if and only if A is a square matrix. Consequently, we cannot compute the square of either of the two matrices Y and W.
There is at least one mistake.
For example, choice (e) should be False.
Y W Z2 = 3 102 7 .
There is at least one mistake.
For example, choice (f) should be True.
There is at least one mistake.
For example, choice (g) should be True.
Correct!
  1. True
  2. False Y W Z2 = 3 102 7 .
  3. False Y W is a 2 × 2 matrix so its square is defined. In fact, (Y W)2 = 363 36 12
  4. False If A is a matrix then A2 is defined if and only if A is a square matrix. Consequently, we cannot compute the square of either of the two matrices Y and W.
  5. False Y W Z2 = 3 102 7 .
  6. True
  7. True