# PROBLEM #2 (4 marks) Consider the linear system x+2y=0 y+2z= k ...

## Transcribed Text

PROBLEM #2 (4 marks) Consider the linear system x+2y=0 y+2z= k (4+k)z=2k = (a) For what value(s) of k is the linear system inconsistent? (b) For what value(s) of k does the linear system have infinitely many solutions? PROBLEM #3 (7 marks) Consider the system of linear equations x1+x3 = b1 2x1-x2+xx=62 - x1+2x2+2x3=63 (a) Write the system as a matrix equation AX = B. (b) Find A-1 the inverse of the coefficient matrix. (c) Use A-1 found in part(b) to solve the system. a (a) For what value(s) of a, b, and C is the matrix 0 1 0 0 in RREF? 0 0 0 1 1 0 5 0 2 1 0 1 4 0 0 -2 (b) If the following matrix is an augmented matrix, then find its solution. 0 0 0 1 -1 3 0 0 0 0 0 0 What is its rank? PROBLEM #2 (4 marks) Consider the linear system x+2y=0 y+2z=k (4+k)z 2k

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