Question

if A is a matrix of order 3*3 and K is a scalar then |KA| =

Answer 1

Answer:

Step-by-step explanation:Let A=$\left[\begin{array}{ccc}a_{1} &b_{1} &c_{1} \\a_{2} &b_{2} &c_{2} \\a_{3} &b_{3} &c_{3} \end{array}\right]$

we need to find |KA|

KA = K$\left[\begin{array}{ccc}a_{1} &b_{1} &c_{1} \\a_{2} &b_{2} &c_{2} \\a_{3} &b_{3} &c_{3} \end{array}\right]$

          =$\left[\begin{array}{ccc}ka_{1} &kb_{1} &kc_{1} \\ka_{2} &kb_{2} &kc_{2} \\ka_{3} &kb_{3} &kc_{3} \end{array}\right]$ (if a matrix is multiplied by a constant,then constant is multiplied to all elements of matrix)

|KA|=$\left|\begin{array}{ccc}ka_{1} &kb_{1} &kc_{1} \\ka_{2} &kb_{2} &kc_{2} \\ka_{3} &kb_{3} &kc_{3} \end{array}\right|$

taking out k from $R_{1},R_{2},R_{3}$    

$k.k.k\left[\begin{array}{ccc}a_{1} &b_{1} &c_{1} \\a_{2} &b_{2} &c_{2} \\a_{3} &b_{3} &c_{3} \end{array}\right]$                           (if each element of row of determinant is                                 multiplied by a constant k, then its value get multiplied by k)

   =$k^{3}$|A|