Given a matrix C of size 4x5 with rank(C) = 3, what is the dimension of its null space? How can you confirm this using MATLAB?

hard📝 Application Q8 of 15

MATLAB - Linear Algebra

Given a matrix C of size 4x5 with rank(C) = 3, what is the dimension of its null space? How can you confirm this using MATLAB?

A3; verify with <code>rank(C)</code>

B2; verify with <code>size(null(C), 2)</code>

C5; verify with <code>size(C, 2)</code>

D4; verify with <code>size(null(C), 1)</code>

Step-by-Step Solution

Solution:

Step 1: Calculate null space dimension
Dimension of null space = number of columns - rank = 5 - 3 = 2.
Step 2: Verify in MATLAB
Use null(C) to get null space basis; its number of columns equals nullity.
Step 3: MATLAB command
size(null(C), 2) returns the null space dimension.
Final Answer:
2; verify with size(null(C), 2) -> Option B
Quick Check:
Confirm rank + nullity = number of columns [OK]

Quick Trick: Nullity = columns - rank; check size(null(C), 2) [OK]

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