True or False?
1.
If \(\{\vec {x}, \vec {y}\}\) is linearly independent, then \(\{\vec {x}, \vec {y}, \vec {x}+\vec {y}\}\) is linearly independent.
True False
2.
If \(\{\vec {x}, \vec {y}, \vec {z}\}\) is linearly independent, then \(\{\vec {y}, \vec {z}\}\) is linearly independent.
True False
3.
If \(\{\vec {y}, \vec {z}\}\) is linearly dependent, then \(\{\vec {x}, \vec {y}, \vec {z}\}\) is linearly dependent.
True False
4.
If \(a\vec {x}+b\vec {y}+c\vec {z}=\vec {0}\), then \(\{\vec {x}, \vec {y}, \vec {z}\}\) is linearly independent.
True False

Source

[Nicholson] W. Keith Nicholson, Linear Algebra with Applications, Lyryx 2021, Open Edition, Problem 5.2.7.