Question 934861
A matrix is given-


{{{(matrix(3,3,2k-1,3,3,3,2k-1,3,3,3,2k-1))}}}

Find value of k when matrix is singular.


A matrix is non-invertable, or singular, when its determinant is zero; so, find its determinant in terms of {{{k}}}, then set that to {{{zero}}} and solve for {{{k}}}.

here, determinant is  {{{D=3+3+2k-1}}}, then we have

{{{3+3+2k-1=0}}}....solve for {{{k}}}

{{{6+2k-1=0}}}

{{{5+2k=0}}}

{{{2k=-5}}}

{{{highlight(k=-5/2)}}} => then we have {{{2k-1=2(-5/2)-1=-5-1=-6}}}

plug this value in given matrix

{{{(matrix(3,3,-6,3,3,3,-6,3,3,3,-6))}}}

check if determinant is equal to zero


*[invoke determinant_of_3x3_matrix -6, 3, 3, 3, -6, 3, 3, 3, -6]