[|2 sin θ cos θ 0]
If A = [-2 cos θ sin θ 0], then
[-1 1 1 ]
what is A(adjA) equal to?
where / is the identity matrix.
This questions was previously asked in
2022 NDA -1 Math
Null matrix
Incorrect AnswerExplanation:
Let’s break it down:
- The matrix A is
```
[ 2sin? cos? 0 ]
[ -2cos? sin? 0 ]
[ -1 1 1 ]
```
- To find A(adjA), remember: For any square matrix A, A * adj(A) = |A| * I, where |A| is the determinant, and I is the identity.
- So, let’s check det(A):
Calculate using the third row, since there are zeros in the third column, it’s quick:
|A| = (2sin? * sin? - cos? * -2cos?) * 1 = (2sin²? + 2cos²?) = 2 (since sin²? + cos²? = 1).
- Therefore, A(adjA) = 2I.
Now, about your options:
- Null matrix: Only when det(A) = 0, which isn’t the case here.
- -I: Only if det(A) = -1.
- I: Only if det(A) = 1.
- 2I (Correct Answer) ? This matches our calculation.
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By: Parvesh Mehta