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Do you have any idea what is matrices in mathematics? Do you think you can pass this matrices quiz? A matrix is basically a rectangular collection or table of numbers, symbols, or expressions that are arranged in rows and columns in mathematics. Take this quiz and learn more about matrices in math. The order for seven matrices is described below. A is a 2x2 matrix. D is a 3x2 matrix. K is a 5x2 matrix. L is a 4x3 matrix. M is a 5x5 matrix. P is a 4x1 matrix. Q is a 1x5 Read morematrixUse this information to answer the true/false statements.
Questions and Answers
1.
What is the determinant for the above matrix?
Explanation ad-bc
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2.
What is the determinant for the above matrix?
Explanation ad-bc
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3.
The order for seven matrices are described below.A is a 2x2 matrix. D is a 3x2 matrix. K is a 5x2 matrix. L is a 4x3 matrix.M is a 5x5 matrix. P is a 4x1 matrix. Q is a 1x5 matrixUse this information to answer the true/false statements below.
4.
I have a square matrix A with a determinant that is not zero.
A.
True
B.
False
Correct Answer B. False
Explanation A times it's inverse is always I - the identity matrix.
A x the inverse of A = the inverse of A x A = I
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5.
What is the determinant for the above matrix?
Correct Answer 3
Explanation Only on Calculator - det(A)
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6.
I have a square matrix A with a determinant that is not zero.
A.
True
B.
False
Correct Answer A. True
Explanation A times it's inverse is always I - the identity matrix.
A x the inverse of A = the inverse of A x A = I
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7.
I have a square matrix A with a determinant that is not zero. I is the identity matrix.
A.
True
B.
False
Correct Answer A. True
Explanation A times it's inverse is always I - the identity matrix.
A x the inverse of A = the inverse of A x A = I
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8.
I have a square matrix A with a determinant that is not zero. I is the identity matrix.
A.
True
B.
False
Correct Answer A. True
Explanation A times it's inverse is always I - the identity matrix.
A x the inverse of A = the inverse of A x A = I
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9.
I have a 2x2 matrix A with a determinant that is not zero. B is 1x2 matrix. I is the identity matrix.
A.
True
B.
False
Correct Answer B. False
Explanation A times it's inverse is always I - the identity matrix.
A x the inverse of A = the inverse of A x A = I
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10.
I have a 2x2 matrix A with a determinant that is not zero. B is 1x2 matrix. I is the identity matrix.
A.
True
B.
False
Correct Answer B. False
Explanation A times it's inverse is always I - the identity matrix.
A x the inverse of A = the inverse of A x A = I
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11.
The determinant for the above matrix is zero. What is the value of x?
Correct Answer 0
Explanation ad-bc = 0 ... so ... substitute the values into the determinant formuata and isolate the x.
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12.
I have a 2x2 matrix A with a determinant that is not zero. B is 1x2 matrix. I is the identity matrix.
A.
True
B.
False
Correct Answer A. True
Explanation A times it's inverse is always I - the identity matrix.
A x the inverse of A = the inverse of A x A = I
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13.
If we call the matrix above 'A', does the inverse of A exist?
A.
Yes
B.
No
Correct Answer B. No
Explanation An inverse exists only for square matrices with a determinant that is not zero. If the determinant is zero, there is no inverse. If the matrix represents a pair of simultaneous equations, it means they are either inconsistent (parallel) or dependent (the same equation).
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14.
The determinant for the above matrix is 15. What is the value of x?
Correct Answer -1
Explanation ad-bc = 0 ... so ... substitute the values into the determinant formuata and isolate the x.
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15.
The order for seven matrices are described below.A is a 2x2 matrix. D is a 3x2 matrix. K is a 5x2 matrix. L is a 4x3 matrix.M is a 5x5 matrix. P is a 4x1 matrix. Q is a 1x5 matrixUse this information to answer the true/false statements below.
16.
The order for seven matrices are described below.A is a 2x2 matrix. D is a 3x2 matrix. K is a 5x2 matrix. L is a 4x3 matrix.M is a 5x5 matrix. P is a 4x1 matrix. Q is a 1x5 matrixUse this information to answer the true/false statements below.
17.
The order for seven matrices are described below.A is a 2x2 matrix. D is a 3x2 matrix. K is a 5x2 matrix. L is a 4x3 matrix.M is a 5x5 matrix. P is a 4x1 matrix. Q is a 1x5 matrixUse this information to answer the true/false statements below.
18.
The determinant for the above matrix is -15. What is the value of x?
Correct Answer 2
Explanation ad-bc = 0 ... so ... substitute the values into the determinant formuata and isolate the x.
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19.
If we call the matrix above 'A', does the inverse of A exist?
A.
Yes
B.
No
Correct Answer A. Yes
Explanation An inverse exists only for square matrices with a determinant that is not zero. If the determinant is zero, there is no inverse. If the matrix represents a pair of simultaneous equations, it means they are either inconsistent (parallel) or dependent (the same equation).
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20.
Select all the statements which are true below
A.
Only square matrices have an inverse
B.
All square matrices have an inverse
C.
All Matrices with a determinant that is not zero have an inverse
D.
Some Matrices with a negative determinant have no inverse
E.
All Matrices with a determinant of zero have no inverse
F.
All matrices with a determinant of zero are inconsistent
G.
All Matrices with a determinant of zero have an infinite number of solutions
Correct Answer(s) A. Only square matrices have an inverse C. All Matrices with a determinant that is not zero have an inverse E. All Matrices with a determinant of zero have no inverse
21.
Matrix A and Matrix D are equal matrices
A.
True
B.
False
Correct Answer B. False
Explanation The statement "Matrix A and Matrix D are equal matrices" is false. This means that Matrix A and Matrix D are not equal to each other. They may have different dimensions, different elements, or both.
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22.
The determinant for the matrix above is 44. The missing number is a value between 1 and 5 inclusive. What is the missing value
Correct Answer 5
Explanation Trial and error. You don't know how to find the determinant manually, so you simply create the matrix, then substitute 1, 2, 3, 4 and 5 into the missing space. Using the det() command is the fastest way to do it. It's faster than the Inverse App if you simply put your matrix inside the brackets.
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23.
P is a row matrix.
A.
True
B.
False
Correct Answer B. False
Explanation The given statement is "P is a row matrix." The correct answer is False. This means that P is not a row matrix. A row matrix is a matrix with only one row. Since the statement says that P is a row matrix, but the correct answer is False, it implies that P is not a row matrix, meaning it has more than one row.
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24.
AK is undefined, but KA is defined.
A.
True
B.
False
Correct Answer A. True
Explanation This statement implies that there is a difference in the definitions of AK and KA. While KA is defined, meaning there is a clear understanding or explanation for it, AK is undefined, suggesting that there is no known definition or explanation for it. Therefore, the statement is true, as it confirms that KA is defined while AK is not.
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25.
The determinant for the matrix above is 26. The missing number is a value between 0 and 5 inclusive. What is the missing value?
Correct Answer 2
Explanation Trial and error.
You can use algebra to solve this but its faster to use the det() command and just substitute the one missing value in each time. It's faster than the Inverse App if you simply put your matrix inside the brackets.
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26.
AK is undefined, but KA is defined.
A.
True
B.
False
Correct Answer A. True
Explanation The statement suggests that the value of AK is undefined, meaning it does not have a specific value assigned to it. On the other hand, KA is defined, indicating that it has a specific value assigned. Therefore, the statement is true because it states a valid comparison between the undefined value of AK and the defined value of KA.
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27.
Matrix K has a determinant of 3.
A.
True
B.
False
Correct Answer B. False
Explanation Only a square matrix can have an inverse, and therefore on square matrices have a determinant.
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28.
The product matrix of DA will be a 2x3 matrix
A.
True
B.
False
Correct Answer B. False
Explanation 3x2 & 2x2 = will give a 3x2 not a 2x3
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29.
The element could be the value 5.
A.
True
B.
False
Correct Answer B. False
Explanation D is a 3x2 matrix, which would have no value d2,3 as there are not 3 columns.
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30.
There are two matrices for which a determinant may be derived
A.
True
B.
False
Correct Answer A. True
Explanation 3x2 & 2x2 = will give a 3x2 not a 2x3
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31.
The matrix multiplication of QK would deliver a product matrix with the order 1x2
A.
True
B.
False
Correct Answer A. True
Explanation 3x2 & 2x2 = will give a 3x2 not a 2x3
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32.
P is a row matrix.
A.
True
B.
False
Correct Answer B. False
Explanation 3x2 & 2x2 = will give a 3x2 not a 2x3
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33.
Q is a column matrix.
A.
True
B.
False
Correct Answer B. False
Explanation 3x2 & 2x2 = will give a 3x2 not a 2x3
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34.
What is the determinant for the above matrix?
Correct Answer -2
Explanation ad-bc
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