Exercises 1 and 2 use the notation for matrices in echelon form. Suppose each matrix represents the augmented matrix for a system of linear equations. In each case, determine if the system is consistent. If the system is consistent, determine if the solution is unique. 1) a) ∎∗∗∗ 0∎∗∗ 00∎0 b) 0∎∗∗∗ 00∎∗∗ 0000∎ 2) a) ∎∗∗ 0∎∗ 000 b) ∎∗∗∗∗ 00∎∗∗ 000∎∗ In Exercises 3 and 4, determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 3) 23h 467 4) 1−3−2 5h−7 In Exercises 5 and 6, choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. Give separate answers for each part. 5) x1+hx2=2 4x1+8x2=k 6) x1+3x2=2 3x1+hx2=k
Exercises 1 and 2 use the notation for matrices in echelon form. Suppose each matrix represents the augmented matrix for a system of linear equations. In each case, determine if the system is consistent. If the system is consistent, determine if the solution is unique.
1) a) ∎∗∗∗ 0∎∗∗ 00∎0
b) 0∎∗∗∗ 00∎∗∗ 0000∎
2) a) ∎∗∗ 0∎∗ 000
b) ∎∗∗∗∗ 00∎∗∗ 000∎∗
In Exercises 3 and 4, determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system.
3) 23h 467
4) 1−3−2 5h−7
In Exercises 5 and 6, choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. Give separate answers for each part.
5) x1+hx2=2 4x1+8x2=k
6) x1+3x2=2 3x1+hx2=k
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