Description
Problem 1.1: (1.3 #4. Introduction to Linear Algebra: Strang) Find a combination x1w1 + x2w2 + x3w3 that gives the zero vector:
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 1 4 7
w1 = ⎣ 2 ⎦ w2 = ⎣ 5 ⎦ w3 = ⎣ 8 ⎦ .
3 6 9
Those vectors are (independent)(dependent).
The three vectors lie in a . The matrix W with those columns
is not invertible.
⎡ ⎤ ⎡ ⎤ 1 2 0 3
Problem 1.2: Multiply: ⎣ 2 0 3 ⎦ ⎣ −2 ⎦.
4 1 1 1
Problem 1.3: True or false: A 3 by 2 matrix A times a 2 by 3 matrix B
equals a 3 by 3 matrix AB. If this is false, write a similar sentence which is
correct.
1
