Let A denote the incidence matrix of the disconnected graph shown in Figure 5.3. Use the

Chapter 3, Problem 2

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QUESTION:

Let A denote the incidence matrix of the disconnected graph shown in Figure 5.3. Use the geometry of the graph to answer the following. a. Give a basis for N(AT). b. Give a basis for N(A). c. Give the equations y must satisfy if y = Ax for some x.

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QUESTION:

Let A denote the incidence matrix of the disconnected graph shown in Figure 5.3. Use the geometry of the graph to answer the following. a. Give a basis for N(AT). b. Give a basis for N(A). c. Give the equations y must satisfy if y = Ax for some x.

ANSWER:

Step 1 of 5

The graph in figure 5.3 is given below.

Corresponding incidence matrix is

Then,

To find the basis for the null space of , let us solve the equation

The row reduced echelon form of is

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