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Chemical Engineering Hand Written_Notes_Part_59

# Chemical Engineering Hand Written_Notes_Part_59 - 120 3...

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120 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES if vector x is a solution of the system A x = b , then ( x + α x ) is also a solution for any scalar α , i.e. A ( x + α x ) = b Also, fi nd dimensions of row space and column space of A. (6) If product of two matrices yields null matrix, i.e. AB = [0] , show that column space of B is contained in null space of A and the row space of A is in the left null space of B. (7) Why there is no matrix whose row space and null space both contain the vector x = h 1 1 1 i T (8) Find a 1 × 3 matrix whose null space consists of all vectors in R 3 such that x 1 + 2 x 2 + 4 x 3 = 0 . Find a 3 × 3 matrix with same null space. (9) If V is a subspace spanned by 1 1 0 ; 1 2 0 ; 1 5 0 fi nd matrix A that has V as its row space and matrix B that has V as its null space. (10) Find basis for each of subspaces and rank of matrix A (a) A = 0 1 2 3 4 0 1 2 4 6 0 0 0 1 2 = LU = 1 0 0 1 1 0 0 1 1 0 1 2

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