 # 1.1 Question 1 Consider a set of four linear equations with three ...

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1.1 Question 1 Consider a set of four linear equations with three unknowns that can be written in matrix form as 1 2 1 1 -2 4 -2 x1 1 -1 2 x2 2 x3 1 a 1 where the coefficient matrix (shown above) is denoted K and the augmented matrix is denoted T. Find the most general solution for X1, X2, and X3 if a = 4, b= 0 and C = - -2. 1.2 Question 2 Consider the matrix = Find A² and show that 3I - 11A + 8A² = 0 where I is the 2 x 2 identity matrix. 1.3 Question 3 Consider the matrix 0.5 0.2 0.3 L= 0.5 0.2 0.2 0.0 0.5 0.5 If you are told that the below matrix is the inverse for (I-L), where I is the identity matrix, what is the value of r (justify your answer)? 12 10 r (I - - L)-1 - = 10 10 10 10 10 12

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