(adsbygoogle = window.adsbygoogle || []).push({}); LINEAR ALGEBRA: 3 vecotrs in R^4 (with 6 variables) -- Are they linearly independent?

For which values of the constants a, b, c, d, e, anf f are the following vectors linearly independent? Justify your answer.

[tex]\left[\begin{array}{c}a\\0\\0\\0\end{array}\right],\,\,\left[\begin{array}{c}b\\c\\0\\0\end{array}\right],\,\,\left[\begin{array}{c}d\\e\\f\\0\end{array}\right][/tex]

I figure that one would setup an equation:

[tex]x\,\left[\begin{array}{c}a\\0\\0\\0\end{array}\right]\,\,+\,\,y\,\left[\begin{array}{c}b\\c\\0\\0\end{array}\right]\,\,+\,\,z\,\left[\begin{array}{c}d\\e\\f\\0\end{array}\right]\,\,=\,\,\left[\begin{array}{c}0\\0\\0\\0\end{array}\right][/tex]

[tex]x\,a\,\,+\,\,y\,b\,\,+\,\,z\,d\,\,=\,\,0[/tex]

[tex]\,\,\,\,\,\,\,y\,c\,\,+\,\,x\,e\,\,=\,\,0[/tex]

[tex]\,\,\,\,\,\,\,\,\,\,\,\,\,\,z\,f\,\,=\,\,0[/tex]

How does one proceed?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: LINEAR ALGEBRA: 3 vecotrs in R^4 (with 6 variables) - Are they linearly independent?

**Physics Forums | Science Articles, Homework Help, Discussion**