Modern Business Statistics with Microsoft (R) Office Excel (R) (with XLSTAT Education Edition Printed Access Card)
Master STK120 with Confidence! Stressed about acing your STK120 exams and tests? We've got the ultimate study pack to boost your understanding and exam performance. Our comprehensive collection of past STK120 tutorial papers and detailed memos provides valuable insights into exam format, key c...
1. 𝑊 + 3𝐼 =
2. 𝑇𝑍 =
3. Calculate the value of 𝑞 that will make 𝐷 singular.
4. Calculate the determinant of 𝑊.
5. Investigate the following properties of determinants for matrix 𝑇:
5.1 Show that |𝑇| = |𝑇 |
5.2 Interchange row 1 and 2 of 𝑇, and show that the sign of the determinant changes but
not the numeric value.
5.3 Multiply the second column of 𝑇, with 4 and investigate whether the value of the
determinant changes 4 – fold.
5.4 Subtract each element of row 2 from the corresponding element of row 1, show that
the value of the determinant remains the same.
5.5 Substitute column 2 with 12 and 6, so that column 2 is a multiple of column 1. Show
that the determinant of the new matrix is zero.
Questions 6 to 10 are based on the following information:
A coffee shop supplies cocktail muffins, cocktail cupcakes and sausage rolls (per dozen) for
the year end functions of three different departments. The order (per dozen) for the functions
is as follows:
Refreshments (Quantities per dozen)
Department Cocktail Cocktail Total income
Sausage rolls
muffins cupcakes
Department A 4 6 10 580
Department B 0 9 20 910
Department C 10 4 0 320
Price (Rand per dozen) 𝒑𝟏 𝒑𝟐 𝒑𝟑
The prices (in Rand per dozen) of the refreshments are given by: 𝑷 = (𝒑𝟏 𝒑𝟐 𝒑𝟑 )
𝟒 𝟔
𝟏𝟎 𝟓𝟖𝟎
Let: 𝑨= 𝟎 𝟐𝟎 be the quantity matrix and 𝑩 = 𝟗𝟏𝟎 the vector that denotes the
𝟗
𝟏𝟎 𝟒
𝟎 𝟑𝟐𝟎
𝟏 𝟒 −𝟐 −𝟏. 𝟓
total income, 𝑬 = 𝟏 , |𝑨| = −𝟐𝟎 𝐚𝐧𝐝 𝑨 𝟏 = −𝟏𝟎 𝟓 𝟒
𝟏 𝟒. 𝟓 −𝟐. 𝟐 −𝟏. 𝟖
6. The total number of refreshments ordered per department in matrix notation is:
7. If the quatities ordered for Department A doubles and the quantities for Department B is
the same as for Department C, the determinant of the altered matrix 𝑨 is:
8. Write down the set of linear equations that can be used to calculate the prices (in Rand
per dozen) of the refreshments.
9. Calculate the price (in Rand per dozen) of cocktail muffins using Cramer’s rule.
10. Calculate the price (in Rand per dozen) of cocktail cupcakes using the inverse matrix
approach.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller thembisilemagudulela. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.98. You're not tied to anything after your purchase.
