Math 1104C, 1104J: Test # 1, Due Feb. 9 11:59, 2022

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1. (5 points) Use Gauss-Jordan elmination to find all solutions to the linear system:

x1 + 3x2 + 2x3 + 4x4 = 2

x3 + x4 = 2

2x1 + 6x2 + 3x3 + 7x4 = 2

2. (5 points) Let

A =

XXXXXXXXXX 0

XXXXXXXXXX

~b =

11

1

Find the reduced row echelon form of (A|~b). Use it to find a solutions to A~x = ~b.

3. (5 points) Solve the system A~x = ~0 using the matrix A from question 5.

4. (6 points) Let A =

(

1 0 −1

1 1 1

)

. Is ~b =

(

3

2

)

in the span of the columns of A? Is ~w =

(

−1 1 1

)

in

the span of the rows of A?

5. (6 points) Let

A =

(

3 −1 2

−1 2 4

)

, B =

1 2−1 −2

0 3

, C = (0 1

1 0

)

Evaluate the following expressions if they make sense.

(a) CB

(b) BC

(c) AB + C

(d) BA + C

(e) CT + C

(f) B + AT

6. (3 points) Give an example of a matrix M where MMT and MTM are not equal matrices.

7. (5 points) Is

P =

(

8 1

5 −2

)

a linear combination of the three matrices

Q1 =

(

1 1

1 1

)

, Q2 =

(

0 1

−1 0

)

, Q3 =

(

1 0

0 −1

)

8. (5 points) Find the inverse of the following matrix: 1 1 −10 1 1

0 1 −1

Page 2

Answered Same DayFeb 09, 2022

linear alge

a

a

SOLUTION.PDF## Answer To This Question Is Available To Download

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