[M] Let An be the n × n matrix with 0’s on the main

Chapter 2, Problem 1E

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QUESTION:

In Exercises l and 2, compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let

\(\begin{array}{l}A=\left[\begin{array}{rrr}2 & 0 & -1 \\ 4 & -5 & 2\end{array}\right], \quad B=\left[\begin{array}{rrr}7 & -5 & 1 \\ 1 & -4 & -3\end{array}\right], \\ C=\left[\begin{array}{rr}1 & 2 \\ -2 & 1\end{array}\right], \quad D=\left[\begin{array}{rr}3 & 5 \\ -1 & 4\end{array}\right], \quad E=\left[\begin{array}{r}-5 \\ 3\end{array}\right]\end{array}\)

-2 A, B-2 A, A C, C D

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QUESTION:

In Exercises l and 2, compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let

\(\begin{array}{l}A=\left[\begin{array}{rrr}2 & 0 & -1 \\ 4 & -5 & 2\end{array}\right], \quad B=\left[\begin{array}{rrr}7 & -5 & 1 \\ 1 & -4 & -3\end{array}\right], \\ C=\left[\begin{array}{rr}1 & 2 \\ -2 & 1\end{array}\right], \quad D=\left[\begin{array}{rr}3 & 5 \\ -1 & 4\end{array}\right], \quad E=\left[\begin{array}{r}-5 \\ 3\end{array}\right]\end{array}\)

-2 A, B-2 A, A C, C D

ANSWER:

Problem 1E

[M] Let An be the n × n matrix with 0’s on the main diagonal and 1’s elsewhere. Compute  for n = 4, 5, and 6, and make a conjecture about the general form of  for larger values of n.

Solution:

Step 1 of 1

For ,



Taking
and in augmented form, we get

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