Let A =3 6 1 1 Express A as a product of elementary matrices. Express A^-1 as a

Question

Let A =3 6 1 1 Express A as a product of elementary matrices. Express A^-1 as a product of elementary matrices. Let A = 2 1 2 1 2 2 1 2 4 and B = 2 2 2 1 2 2 1 2 4. Compute the LU decomposition if it exists. If the LU decomposition does not exists, then explain why. See pg 67-68 of the text. A square matrix is called nilpotent if A^k = 0 for some positive integer power k. Show that if A is nilpotent then I - A is invertible. See problem 20 on page 59 for a hint. If A is nilpotent, must I + A be invertible? Prove your answer. REF of a matrix containing a variable. Example: The matrix A(t) = 1 -t 1 1 1-t has REF 1 0 1 -t t^2 - 2t.. This means A is singular when t = 0 or f = 2. and A is nonsingular for all other values of t. The following examples are similar. There are some values of t where A is singular, others where it is nonsingular. Determine values of t where the matrix is singular, and values of t where A is nonsingular. 1 -t 2 2 1 - t t -9 1 t + 6 Determinant of a matrix containing a variable. Compute the determinant of the matrices from the previous problem, and solve the equation det A(t) = 0. Compare the results for both matrices.

Explanation / Answer

Except B all answers you wrote correctly

the abswer for b is

CH3-CH2-CH2-CH(OH)-CH3 ( 2-pentanol)

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