Instructions Try to Answer all Please These are true or fals

Instructions Try to Answer all Please. These are true or false questions please give reason to support why it is true or false

Matrices in Algebra

Solution

1. True. Numerical errors arise during computations due to round-off errors and truncation errors.

Computational error = truncation error + round-off error

Hence computation error is the sum of truncation and rounding error.

2. False. The correct property of norms of a matrix is:-

||A+B|| <= ||A|| + ||B||

3. True. This is becuase we can write

e^x +1 =0

=> e^x = -1

=> x = i(2npi +pi) , n belongs to integers

4. True. Problem is sensitive or ill-conditioned, if cond >> 1 i.e. Problem is sensitive or ill-conditioned, if relative change in solution can be much larger than that in input

5. False. The transpose of a permutation matrix is its inverse i.e.

P^T = P^-1

=> PP^T = I