Given matrix D = [1 2 3; 4 5 6; 7 8 9], write MATLAB code to find a vector in the null space and verify it satisfies D * x = 0. What is the correct approach?

hard📝 Application Q9 of 15

MATLAB - Linear Algebra

Given matrix D = [1 2 3; 4 5 6; 7 8 9], write MATLAB code to find a vector in the null space and verify it satisfies D * x = 0. What is the correct approach?

Ax = null(D); verify with norm(D*x) == 0

Bx = inv(D); verify with D*x == 0

Cx = rank(D); verify with D*x == 0

Dx = det(D); verify with norm(D*x) == 0

Step-by-Step Solution

Solution:

Step 1: Find null space vector
Use null(D) to get basis vectors for null space.
Step 2: Verify null space property
Multiply D * x and check if result is zero vector using norm(D*x) == 0.
Final Answer:
x = null(D); verify with norm(D*x) == 0 -> Option A
Quick Check:
null(D) gives null space; norm(D*x) checks zero vector [OK]

Quick Trick: Use null(D) and check norm(D*x) == 0 to verify [OK]

Common Mistakes:

Using inv(D) instead of null(D)
Using rank(D) as vector
Using determinant for null space

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Given matrix D = [1 2 3; 4 5 6; 7 8 9], write MATLAB code to find a vector in the null space and verify it satisfies D * x = 0. What is the correct approach?

Step 1: Find null space vector

Step 2: Verify null space property

Final Answer:

Quick Check:

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