(a) Create the following matrix and put the answer in p4a. Do not input element by element. egin{bmatrix} 1 & 3 & 0 & 0 & 0 & 0 & 0 & 0 & 3 & 1 \ 2 & 4 & 0 & 0 & 0 & 0 & 0 & 0 & 4 & 2 \ 0 & 0 & 1 & 3 & 0 & 0 & 3 & 1 & 0 & 0 \ 0 & 0 & 2 & 4 & 0 & 0 & 4 & 2 & 0 & 0 \ 0 & 0 & 0 & 0 & 1 & 3 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 0 \ 0 & 0 & 3 & 1 & 0 & 0 & 1 & 3 & 0 & 0 \ 0 & 0 & 4 & 2 & 0 & 0 & 2 & 4 & 0 & 0 \ 3 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 \ 4 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 4 end{bmatrix}
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Step 1
1) Create the matrix A: A = [1 3 0 0 0 0 0 0 3 1 2 4 0 0 0 0 0 0 4] Show more…
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For $I_{2}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right], I_{3}=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right],$ and $I_{4}=\left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right],$ show $A I=I A=A$ for the matrices of like size. Use a cal for Exercise 14. $$\left[\begin{array}{rr} -3 & 8 \\ -4 & 10 \end{array}\right]$$
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a. A matrix with aij = 2i - j b. A matrix with ai = (-1)^j c. B = [bilzx4] with bij = (~ l)i+i d. B = [bij]3x4 with bij = 1 if i < j and bij = 0 if i ≥ j C = [ci]4x3 with Cij = i + j if i < j and Cij = 0 if i ≥ j C = [cij]4x3 with Cij = 0 if i ≠j and Cij = 1 if i = j
Supreeta N.
Find the Jordan canonical form $J$ for the matrix $A$. You need not determine an invertible matrix $S$ such that $S^{-1} A S=J$. $A=\left[\begin{array}{llllllll}1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{array}\right]$.
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