![3. Let B= (a) [2 marks] Find the Trace of B. (b) [4 marks) Find B-1, the inverse of B. (c) [4 marks] A vector 7 is an eigenve](http://img.homeworklib.com/questions/49898520-c89f-11eb-8acb-c956a31a6856.png?x-oss-process=image/resize,w_560)
3. Let \(\quad B=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]\).
(a) Find the Trace of B.
(b) Find \(B^{-1}\), the inverse of \(B\).
(c) A vector \(\vec{v}\) is an eigenvector of the matrix \(B\) if Matrix-Vector Multiplication \(B \vec{v}\) results in a scaling of the vector \(\vec{v}\). (i.e. \(B \vec{v}=c \vec{v}\), with \(c\) a real number.) Using the definition of Matrix-Vector Multiplication show that the vector \(\vec{v}=\left[\begin{array}{l}1 \\ 1\end{array}\right]\) is an eigenvector of \(B\) with eigenvalue \(c=3\).
Homework Answers
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two seperate questions multiple choice
Determine if the vector is an eigenvector of a matrix. If it is, determine the corresponding eigenvalue. A= 1 1 1 and v The eigenvalue is 2. The eigenvalue is 0. The eigenvalue is 3. v is not an eigenvector. Find the inverse of the matrix, if it exists. A= -1-6 6 3 2 11 11 1 11 33 33 NE -= 2 11 = -18 = -1= 야야 O
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