GCSE Mathematics Question Analysis Topic: Mathematics - Matrices
Exam Questions:
1) If A is a 3×3 matrix such that |A|=8, then |3A| equals:
A) 8
B) 24
C) 72
D) 216
2) If A is a skew symmetric matrix of order 3, then the value of |A| is
A) 3
B) 0
C) 9
D) 27
Answer:
For GCSE Mathematics, you should know:
1) Since we are given |A| = 8,
we can deduce that |kA| = kn|A| (n is A's order)
As such, |3A| = 33|A| = 33 x 8 = 27 x 8 (as A is a 3 by 3 matrix)
= 216. Hence, (D) is the right answer.
2) A is a skew symmetric matrix, i.e. AT = -A
==> | - A | = (-1)n|A|, where n is the order.
Substituing 3 in, we get -|A|.
Substituting into (i),
|AT| = -|A|
==> -|A| = |AT| (ii)
For any matrix,
|A| = |AT|
Replacing these into (ii),
|A| = -|A|
==> 2|A| = 0
==> |A| = 0
Work hard for your GCSE Mathematics examination!
End of analysis. Great!