Determine the values of h such that the matrix is the augmented matrix of a consistent linear system

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Section 1.1, #19

"In exercises 19-22, determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system."

All problems used are subject to fair use. Problems taken from "Linear Algebra and Its Applications" by David C. Lay, Steven R. Lay, and Judi J. McDonald.
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It is hands down the most in-depth explanation to an answer, I hope I ace my test tomorrow.

PratikGurung-xy
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Just noticed a small error in #19. Row 1 should be: [-3 -3h -12]. This shouldn’t change the answer though.

mathmagician
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Linear Algebra's tricky sometimes! Thanks for the help!

patrickmayer