## Linear Algebra and Its Applications, exercise 1.2.5

Exercise 1.2.5. The following three equations: $\setlength\arraycolsep{0.2em}\begin{array}{rcl} t&=&0 \\ z&=&0 \\ x + y + z + t&=&1 \end{array}$

correspond to planes in 4-space (or space-time). Find two points on the line that is the intersection of the planes represented by the equations.

Answer: We substitute the values of t and z from the first two equations into the third: $x + y + z + t = 1 \Rightarrow x + y = 1$

Values of x and y satisfying this equation include x = 1, y = 0 and x = 0, y = 1. Two points satisfying all three equations are thus (1, 0, 0, 0) and (0, 1, 0, 0).

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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### 1 Response to Linear Algebra and Its Applications, exercise 1.2.5

1. Trevor Stern says:

Thank you very much for posting these exercises in Linear Algebra and It’s Applications. You are a godsend!