Consider the linear transformation T: R³ R³ defined by: T(v) = Av where A is the matrix: 1 0 1 00-2 0 1 0 A Find all eigenvalues and their corresponding eigenvectors for A. • Is A diagonalizable? If so, diagonalize A. If not, explain in complete sentences why not.

Solve the system of differential equations. x1 = 3x₁1x2 (x₂² = 1x₁ + 5x2 18 x₁ (0) = 10, x₂(0) x₁ (t) = x₂(t) = Question Help: Message instructor Submit Question =

linear equation

Examine the given solution below. (a) ldentify at what line/s contain errors in solving, (b) explain why these are wrong, and (c) rewrite all the line/s containing errors this time showing the correct solutions. [20] The goal is to evaluate G- 12* + e -2z de By the Fundamental Theorem of Calculus, we have: 1 dz - 2x2 dx = 122 dr + 25 dz +e e 2x2 - 6z + 2 = -2r 1 11 = -2(5 – 1)- - 6(5 – 1)2 +e -2(5-1)