Search & Filtering
Compare and contrast South African government expenditure trends with other global economies
over the past 10 – 15 years
Research topic: Explore the development of literacy skills in the Foundation Phase.
Use the following Key takeaways to write a problem Statement.
1. A statement of the problem is used in research work as a claim that outlines the problem addressed by a study.
2. A good research problem should address an existing gap in knowledge in the field and lead to further research.
3. To write a persuasive problem statement, you need to describe (a) the ideal, (b), the reality, and (c) the consequences.
[ 1 0 -1
3. Consider the matrix A = 0 3 0
-1 0 1 ]
- Find the eigenvalues of A.
- Find the eigenspaces corresponding to each eigenvalue from A.
2. Consider a linear transformation T: R3 → R3 defined by
([x [ x + 4y +3z
T y = -5y - 4z
z]) 5x + 10y + 7z ]
Note: T is a 3x1 matrix containing x, y, z respectively. T is equal to another matrix as shown above.
a) Find the matrix A for T
b) Find a basis for ker(T) and the dim(ker(T)). Then find dim(Im(T)), without finding a basis for Im(T). (Show all working)
c) Find a basis for Im(T)
Deregulation within the airline industry was introduced in South Africa in 1991. Before deregulation, South African Airways (SAA) was the only service provider.
There are several factors in the business world that apply pressure to a modern-day organisation such as SAA. Which one of these factors is depicted in the mini-case study above?
Research topic: Explore the development of literacy skills in the Foundation Phase.
Use the following methods to frame research’s context:
1. Describe the field (the area you will be investigating, for example, discipline problems)
you’ll be exploring in a few words.
2. Describe the significance of this field.
3. Describe the current “hot issues” or “trending subjects” in this field.
4. Describe the exact region of the field you will be studying.
5. Describe how your suggested study would advance the field.
6. Summarize the field’s current research foundation and highlight the gaps your study aims
to fi
- Answer the following questions
→ → → [ 1
a) Consider the linear transformation T(x) = proju(x), where u = 0
3 ]
Find the matrix for T.
b) Find the matrix for the linear transformation which reflects every vector in R2 across the x-axis and then rotates every vector through an angle of 𝝅/6. (Show all working)
EXERCISE 2: Find the rank and the nullity of the linear transformation S: p_1→ℝ given by
S(p(x)) = ∫_0^1p(x)dx.
