Q12. [4 marks] Answer the following with either True or False. You do not need t
ID: 3117429 • Letter: Q
Question
Q12. [4 marks] Answer the following with either True or False. You do not need to give a reason for your answer. a) If A is a square matrix, then B =-(A + A") is a symmetric matrix. 1-1 5 2 7 b) The vector u = | 3 | is in the Null-space of A = c) If two square matrices A and B are similar, then det(A) = det(B). d) If A is a 7 × 9 matrix with nullity(A) = 2, then the rank of A is 9. e) If a square matrix A is diagonalizable, then A always has distinct eigenvalues. f) If A is an invertible matrix, then 0 is not an eigenvalue of A. g) For a given n × n matrix A such that the equation Ax-0 has only trivial solution, then A is invertible. h) S-p(t) E Pal p (0) = 1} is a subspace of P2, the space of all polynomials of degree 2 or less.Explanation / Answer
A)True
if A is square matrix then the given B is also symmetric matrix.
B)True,
The given u is the null space of given Matrix A
C) true
If two matrix are similar then the determinant of both matrix are similar.
D) False
Since the matrix of 7*9 has nullify of 2 then the rank of matrix is 5 not 9 .
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