MATH111 HW 4
Due Date: 8th Oct, 2007 (Mon) Please hand in your homework in my tutorial or putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26) 1374 0 5 9 6 Ch2.3 # 8 Determine if the matrix 0 0 2 8 is invertible. Use as few calcula0 0
MATH111 Additional Problems: Solution
The problems are quite difficult if your goal is just a pass for the midterm.
1. A n n matrix A is called upper triangular if aij = 0 whenever i > j . Prove that the product of two upper triangular matrices is upper t
MATH111 Additional Problems
The problems are quite difficult if your goal is just a pass for the midterm.
1. A n n matrix A is called upper triangular if aij = 0 whenever i > j . Prove that the product of two upper triangular matrices is upper triangular.
MATH111 Quiz 2B Solution
1. Let T : R83 R38 be a linear transformation with standard matrix A. Determine if T is one-to-one; or onto; or both one-to-one and onto; or both are not one-to-one or onto; or just impossible. a. A has 83 pivot positions. b. A ha
MATH111 Quiz 1B Solution
1. [4] For each matrix below, determine whether its columns form a linearly independent set. Give reasons to your answers.(Avoid calculation if possible.) 4 12 1 5 3 2 a. 1 3 b. 0 4 9 18 0 0 00 00 4 12 4 12 0 (a) 1 3 0 0 0 0 0 As
MATH111 Midterm Summary
A system of equations is consistentThe system has a solution.(Unique or Innitely many) There are 3 types of elementary row operations. Multiplying the row by a non-zero constant Interchanging two rows One row plus or minus a scala
MATH111 HW 7
Due Date: 29th, Oct, 2007 (Mon) Please hand in your homework in the tutorial session or by putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26). Ch 2.9 # 6 In the following exercise, the vector x is in a subspace H with a
MATH111 HW 6
Due Date: 22nd, Oct, 2007 (Mon) Please hand in your homework in the tutorial session or by putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26). Ch 3.3 # 6 Usec Cramers rule to compute the solutions of the system 2x1 x1 3x
MATH111 HW 5
Due Date: 15th, Oct, 2007 (Mon) Please hand in your homework in the tutorial session or by putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26). Ch 3.2 # 10 Find the following determinant by row reduction to echelon form.
MATH111 HW 3
Due Date: 2nd, Oct, 2007 (Tue) Please hand in your homework by putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26) Ch1.9 # 14 Let T : R2 R2 be the linear transformation with standard matrix A = [a1 a2 ], where a1 and a2 a
MATH111 HW 2
Due Date: 24th, Sept, 2007 (Mon) Please hand in your HW to me in my tutorial session or Put it in the collection box outside MATH dept (Rm 3461, Lift 25-26) Ch1.3 # 4 Given u= 3 2 ,v = 2 1
Display the following vectors using arrows on an xy -
MATH111 HW 1
Due Date: 17th, Sept, 2007 (Mon) Please hand in your HW to me in my tutorial session or Put it in the collection box outside MATH dept (Rm 3461, Lift 25-26) Ch1.1 # 2 Solve the following system by using elementary row operations on the equati