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$\operatorname{For} A=\left[\begin{array}{ccc}{1} & {2} & {3} \\ {1} & {2} & {3} \\ {1} & {2} & {3}\end{array}\right],$ find one eigenvalue, with no calculation. Justify your answer.

$A$ is not invertible. Hence, $\lambda=0$ is an eigen value of the matrix $A$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 1

Eigenvectors and Eigenvalues

Vectors

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So in this question, we're gonna find on I get value of a specific A matrix, this matrix being 111 222 That's the one, by the way. 333 Now it's a rule of linear algebra matrices that if a matrix is linearly dependent, I can value is equal to zero. And that's the case here. A is linearly dependent linearly dependent means that the rows or columns are multiples of one another. So in this case, you can see Row one through. Three are exactly the same, meeting their multiples of each other. You can also see this in the columns, so call him three. It's just three times column one calm to It's just two Times column, too. Now it's a rule that if a matrix is a nearly dependent, I can value always equal zero

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