Answer:
I.
A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4
Null space is exactly two dimensional plane
dim null (A) = 2
II.
Rank A = dim U - dim Null A = 5 - 2 = 3
III.
Number of linearly Independent columns of A is the rank of A = 3
IV.
Yes, The system Ax = b has no solution sometimes as range of A \neq V
V.
Yes,Sometimes Ax = b has a unique solution
VI.
Yes, sometimes Ax = b has infinitely many solutions
Step-by-step explanation:
1. (-3/2, 1)
2. (6,-3)
3. (8/3, 2)
4. <u>(</u><u>2</u><u>,</u><u>-4</u><u>)</u>
<u>5</u><u>.</u><u>(</u><u>-3</u><u>,</u><u>-1</u><u>)</u>
<u>6</u><u>.</u><u> </u><u>(</u><u>0</u><u>,</u><u>3</u><u>/</u><u>2</u><u>)</u>
<u>7</u><u>.</u><u> </u><u>(</u><u>4</u><u>,</u><u> </u><u>-2</u><u>)</u>
<u>8</u><u>.</u><u>(</u><u>8</u><u>,</u><u>2</u><u>)</u>
<u>9</u><u>.</u><u> </u><u>(</u><u>0</u><u>,</u><u>0</u><u>)</u>
Answer:
Expert? Sorry, not me, but what sort of questions do you have?
Step-by-step explanation: