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# Matrices a level further maths watch

1. Attachment 516637516639Can someone solve this ques and upload the picture of the solution
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2. (Original post by ja.19)
Attachment 516637516639Can someone solve this ques and upload the picture of the solution
Which part are you struggling on, and what have you tried?
For the first part the rank is the number of linearly independent rows, or equivalently columns of the matrix.
3. The last part where we have to show that there is no vector that satisfies Ax=(0 2 -1 3)
4. (Original post by ja.19)
The last part where we have to show that there is no vector that satisfies Ax=(0 2 -1 3)
You don't need to show that no such vector can exist, only that it can't have all its coordinates positive.
So you suppose where:
with .
Sub in your values for and obtain a contradiction with the inequalities.
Spoiler:
Show
I got this contradiction that .
5. (Original post by joostan)
You don't need to show that no such vector can exist, only that it can't have all its coordinates positive.
So you suppose where:
with .
Sub in your values for and obtain a contradiction with the inequalities.
Spoiler:
Show
I got this contradiction that .
6. Can you help with part 3
7. (Original post by ja.19)
Can you help with part 3
Well if is the vector . Then you know that if is a vector in the null space then: , so you need to find minimise the magnitude of .

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