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Resolved: Practice Exam 1 Q4 answer explanation query
Regarding Practice Exam 1 Q4/6, I am unsure how option 4 was selected as the correct answer. The explanation provided doesn't clearly and fully explain how Matrix A variables were derived and calculated to be 1&0&0\\0&1&0\\0&0&0.8
Is there or can a detailed explanation be provided of how the Matrix A zeros and ones in this particular question were obtained through reference to the case 1 example?
Please advise
Is there or can a detailed explanation be provided of how the Matrix A zeros and ones in this particular question were obtained through reference to the case 1 example?
Please advise
2 answers ( 1 marked as helpful)
Hi Asghar,
So, in this practice exam you are given a 3x1 vector/matrix B that contains the average spending per meal of Bob, in the form:
In question 4, we learn that Bob now has a discount of 20% for dinner and we need to modify B to reflect that. Since the discount is 20%, that means that Bob will spend 80% of his original spending on dinner. Thus, the new vector, let's call it B' should look like this:
In question 4, it is also said that this new vector B' is found by multiplying the original vector B with a matrix. Let's call this matrix C. Now, in the answers all the matrices, except one, are 3x3. Since the result of the multiplication should be 3x1 as well, we know that the only order in which this is possible is if we have CxB, not BxC.
Then, in order to obtain the answer, you can simply try all 4 options and see which one gives us the correct result. Here are the 4 results:
As you can see, only answer 4 give us the desired result.
When you get more experienced working with matrices, you'll have intuition about what each of these mean, without having to calculate all the products. The thing is, in the 3x3 matrices, each row corresponds to the row in the result. We know we want to "select" only the breakfast for the first row in the result - thus, 1 0 0 does exactly that. For the second row, we only want to select the lunch. Thus 0 1 0, gives us lunch. For the third row, we want to have 80% of the dinner - 0 0 0.8 does the job.
In general, if you have such a square matrix with just the diagonal values, the result when multiplying it with a vector of the same size will always be some scaled version of the entries in the original vector. E.g.:
We say there is no interference (i.e. there is no mixing between x, y and z, as well as, a, b and c)
Hope this explains how you can construct the matrix yourself and answer the question.
Let me know if you need further assistance :)
Best,
Nikola, 365 Team
So, in this practice exam you are given a 3x1 vector/matrix B that contains the average spending per meal of Bob, in the form:
In question 4, we learn that Bob now has a discount of 20% for dinner and we need to modify B to reflect that. Since the discount is 20%, that means that Bob will spend 80% of his original spending on dinner. Thus, the new vector, let's call it B' should look like this:
In question 4, it is also said that this new vector B' is found by multiplying the original vector B with a matrix. Let's call this matrix C. Now, in the answers all the matrices, except one, are 3x3. Since the result of the multiplication should be 3x1 as well, we know that the only order in which this is possible is if we have CxB, not BxC.
Then, in order to obtain the answer, you can simply try all 4 options and see which one gives us the correct result. Here are the 4 results:
As you can see, only answer 4 give us the desired result.When you get more experienced working with matrices, you'll have intuition about what each of these mean, without having to calculate all the products. The thing is, in the 3x3 matrices, each row corresponds to the row in the result. We know we want to "select" only the breakfast for the first row in the result - thus, 1 0 0 does exactly that. For the second row, we only want to select the lunch. Thus 0 1 0, gives us lunch. For the third row, we want to have 80% of the dinner - 0 0 0.8 does the job.
In general, if you have such a square matrix with just the diagonal values, the result when multiplying it with a vector of the same size will always be some scaled version of the entries in the original vector. E.g.:
We say there is no interference (i.e. there is no mixing between x, y and z, as well as, a, b and c)Hope this explains how you can construct the matrix yourself and answer the question.
Let me know if you need further assistance :)
Best,
Nikola, 365 Team
Super learner
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Thanks for the detailed explanation through the use of matrices; it helped me understand how the answer was derived much more clearly.
By the way, the question stated that the 20% discount was for dinner and not lunch .
Thanks again
By the way, the question stated that the 20% discount was for dinner and not lunch .
Thanks again