numerical linear algebra

Quiz 5: (Each 5 points) 1) The ve ctor is in a su bspace H with a basis vector = {,} where = [ − ], = [ − − ], = [ − − ]. Find the B co -ordinate vector of . By inspection write another different basis ′of H and find the ′ co -ordinate vector of the same . 2) Find the DETERMINANT of the following matrix : A = [ − − ] Answer the followings . Explain: (i) Is A invertible? (ii) Are the columns of A linearly Independent? 3) Let A = [ √ ] B = [ − ] ANSWER AND EXPLAIN THE FOLLOWING: (i) Is the ma trix invertible? (Do not compute AB) (ii) Solve ( ) = without computing the Matrix AB or its transpose . (iii) What is the dimension of column space of ( )? (Hint: Use Determinant Invertible Matrix Theor em and Rank Theorem )