## Linear Algebra and Its Applications, Review Exercise 1.9

Review exercise 1.9. Show a 2 by 2 system of equations (i.e., two equations in two unknowns) that has an infinite number of solutions.

Answer: One possibility is the following system: $\setlength\arraycolsep{0.2em}\begin{array}{rcrcr}u&+&v&=&0 \\ 2u&+&2v&=&0 \end{array}$

corresponding to the matrix equation $Ax = 0$ where $A = \begin{bmatrix} 1&1 \\ 2&2 \end{bmatrix}$

The solutions to this system include any $(u, v)$ where $v = -u$.

NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.

If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition , Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books .

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