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Suppose a $4 \times 7$ matrix $A$ has four pivot columns. Is Col $A=\mathbb{R}^{4} ?$ Is Nul $A=\mathbb{R}^{3} ?$ Explain your answers.

Thus, the dimension of null space of the matrix is 3 .since, the 3 dimensional vectors may or may not belong to $\mathrm{R}^{3}$ .Thus, the nullity of the matrix is not $\mathrm{R}^{3}$ .

Calculus 3

Chapter 4

Vector Spaces

Section 6

Rank

Vectors

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02:56

In mathematics, a vector (…

06:36

01:39

Suppose a $4 \times 7$ mat…

02:46

Suppose a $5 \times 6$ mat…

04:16

Suppose $A$ is a $3 \times…

06:41

Show that a $3 \times 7$ m…

02:26

If $A$ is a square matrix …

08:21

Show that a $6 \times 4$ m…

03:26

For each matrix, find $A^{…

08:15

Determine the null space o…

Yeah, well, given the metrics air, which is 4 to 7 on our tricks and your tests been Thank you. And and the question that this mattresses were by what columns? So therefore, the diamond Anson column space is your since l 45 columns. Andi, Uh, the question that has been given that we have to find out if the column space is Issa Space off. Uh huh. Who and if in all spaces, a space off our treatment now the first part since Carl, um A is four payments of space off powerful. That is more. There are 45 What elements in call in air So that the dimensional economy is food on hands. It is a subspace apart pores. Therefore, concerts with our work. The worse part. We can agree, uh, call them air. This system is based off powerful Mhm. But the null space off air has diamonds and on minus a rank A which is equal to seven minus any number of columns and seven minus four, which is a good of three. So the diamonds and of knows basis is three. So therefore okay, I think is a three diamonds, another victor space with seven elements since number of columns of seven. So each director has seven elements in it so that our has toe be subspace off, uh, seven. So it cannot be suspects a party.

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