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Homework1: Problem 11 Previous Problem Problem List Next Problem (1 point) Determine the value of h such that the matrix is the augmented matrix of a consistent linear system 4 -21h -16 8 8 Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining Email instructor

Answer 1

Here the augmented matrix is given.we know a system is consistent if rank(augmented matrix)=rank A.so we need to find an h satisfying these condition.for this we first find row reduced echelon form.then find h.answer is h=-2.

[A: B] = [4 -2 h -16 8 8] here A = [4 -2 -16 8] we know a system is consistent if mark a = rank[a: b] use now operations b_0 reduce [a: b] into reduced abelon forms r_1 rightarrow r_1/4 [1 -1/2 h/4 -16 8 8] r_2 rightarrow r_2 + 16r_1 [1 -1/2 h/4 0 0 8 + 4h] rank a = 1 we want rank [a: b] = 1 for this 8 + 4h = 0 4h = -8 h = -8/4 = -2 when h = -2 system is consistent h = -2