If A is a 7 x 3 matrix, what is the smallest possible dimension of Nul A? Explain your answer.

Question

Mathematics

Litzy Duran

13 January, 01:33

If A is a 7 x 3 matrix, what is the smallest possible dimension of Nul A? Explain your answer.

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Answers (1)

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Lincoln Hoover · Answer 1

the smallest possible dimension of Nul A is zero.

Step-by-step explanation:

The given matrix has 7 rows and 3 columns since it is a 7 x 3 matrix.

Rank Nullity Theorem:-

For any matrix A

rank A + dimension of Nul A = Column of A

Here, column of A = 3

Thus, we have

rank A + dimension of Nul A = 3

Since, it is a 7 x 3 matrix, hence the rank of this matrix can be 3.

Therefore, we have

3 + dimension of Nul A = 3

=> dimension of Nul A = 0

Therefore, the smallest possible dimension of Nul A is zero.