Midterm Examination-Linear Algebra Your Name is Your Lucky Number in my class is
ID: 3138728 • Letter: M
Question
Midterm Examination-Linear Algebra Your Name is Your Lucky Number in my class is Your Student ID Number is Try to finish it in 1.5 hours independently. There are 20 questions in total, each gets 5 m For brevity, the symbols R1, R2,... , stand for row 1, row 2, and so on. 1 3 41 1. Let A=1-4 2-6|and b-lb2 (1) Compute Ab, write out the three entries clearly (2) Write out the echelon form of A. How many rows of A contain a pivot position? (3) Is the equation Ax b consistent for all possible bi, b, by ? Why?Explanation / Answer
Add 4 times the 1st row to the 2nd row
Add 3 times the 1st row to the 3rd row
Multiply the 2nd row by 1/14
Add -7 times the 2nd row to the 3rd row
Add -3 times the 2nd row to the 1st row
Then the RREF of A is
1
0
13/7
0
1
5/7
0
0
0
2 rows of A contain a pivot position
3. In view of the RREF of A, the columns of A do not span R3. Hence the equation AX = b is not consistent for all possible b1,b2,b3.
1
0
13/7
0
1
5/7
0
0
0