1.4.11 Matrix Transformations

(Underline {Ext {Condition:}}) Find all the values of the matrix (a = left (egin {array} {ccc} 41 /25 & 0 & 12/25 \ 0 &3 & 0 \ 12 /25 & 0 & 34 / 25end {Array} ight)), check them. After obtaining a characteristic equation, make an audit of its free member (should be (Operatorname {Det} A)) and its coefficient at (lambda^{2}) (should be (Operatorname {TR} A)). When solving this equation, choose the first root (lambda_ {1}), choosing it among the dividers of a free member, and lower the degree of equation, dividing its left part into linear bicneriolers (lambda-lambda_ {1}) “corner” or along the mining.