1.1.23 Vector Algebra

Condition: Find the rank and basis of the vectors system, go to the new basis. Record the decomposition of vectors at the found bases. \ [\ Begin {Array} {l} A_ {1} = \ Left (\ Begin {Array} {l} 1 \\ 1 \\ 2 \ END {Array} \ RIGHT), A_ {2} = \ left (\ begin {array} {l} 2 \\ 1 \\ 1 \ end {array} \ right), a_ {3} = \ left (\ beinin {arry} 3 \\ 2 \\ 2 \\ 2 \ end {Array} \ Right), A_ {4} = \ Left (\ Begin {Array} {l} 4 \\ 3 \\ 6 \ END {Array} \ RIGHT) \\EN) A_ {5} = \ left (\ begin {array} {l} 2 \\ 5 \ end {array} \ right). \ end {Array} \]