Exam (elaborations)
mat1503 exam pack
- Course
- Linear Algebra I (MAT1503)
- Institution
- University Of South Africa (Unisa)
Exam of 14 pages for the course Linear Algebra I at Unisa (mat1503 exam pack)
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1/9/23, 9:12 AM MAT1503-Exam Oct/Nov 2022: Attempt reviewMENU
Started on Tuesday, 15 November 2022, 8:21 AM
State Finished
Completed on Tuesday, 15 November 2022, 9:59 AM
Time taken 1 hour 37 mins
Question 1
Complete
Marked out of 6.00
The value (s) of k for which the matrix
−1 1 k
⎡ ⎤
⎢ 0 1 4⎥
⎣ ⎦
k 3 7
is singular is/are given by:
k = −1 or k = 2
k = 5 or k = 1
k = −1 or k = 0
None of the given option
k = 5 and k = 1
k = −1 or k = 5
Question 2
Complete
Not graded
Given two n × n invertible matrices A and B such that (A − B)(B + A) = A
2 2
− B . Which of the following statement is correct?
None of the given options
−1
B = A BA
A is the inverses matrix of B
−1
B = ABA B
−1
B = BABA
https://cset.myexams.unisa.ac.za/mod/quiz/review.php?attempt=167441&cmid=72761 1/14
, 1/9/23, 9:12 AM MAT1503-Exam Oct/Nov 2022: Attempt review
Question 3
Complete
Marked out of 4.00
MENU
Consider the matrices below with X = AB , where
1 2 −1 4
⎡ ⎤
A = ⎢ 3 −1 1 3 ⎥
⎣ ⎦
−2 5 −k k + 1
and
1 2 −1
⎡ ⎤
⎢ 0 4 1⎥
B = ⎢ ⎥
⎢ 3 −1 1⎥
⎣ ⎦
−2 5 k(k − 1)
For which value(s) of k will the entry X23 be zero?
No such k
k = −2
–
1 ± √5
k =
2
None of the given option
k = 0 or k = 1
k = 3
Question 4
Complete
Marked out of 4.00
Consider the system of linear equations with unknown a, b, and c and λ is parameter to be determined.
2 2
⎧ a + (λ + 1)b − (λ − λ − 8)c = 3 − λ,
⎪
2
⎨a − (λ + 1)b = 3
⎩
⎪
2 2
− (λ + 1)b − (7 + λ − λ )c = λ.
Use elementary row operation to solve the above system. Find the value(s) for λ for which the system has no solution?
λ = −2 and λ = −3
λ = 2 or λ = −3
λ = −2 or λ = 3
None of the given options
https://cset.myexams.unisa.ac.za/mod/quiz/review.php?attempt=167441&cmid=72761 2/14
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