Let `|(x^2+3x,x-1,x+3),(x+1,-2x,x-4),(x-3,x+4,3x)| = ax^4 + bx^3 + cx^2 + dx + e `be an identity in x, where a, b, c, d, e are independent of x. Then, the value of e isA. 4B. 0C. 1D. none of these

Let `|(x^2+3x,x-1,x+3),(x+1,-2x,x-4),(x-3,x+4,3x)| = ax^4 + bx^3 + cx^

1.	Let `\|(x^2+3x,x-1,x+3),(x+1,-2x,x-4),(x-3,x+4,3x)\| = ax^4 + bx^3 + cx^2 + dx + e `be an identity in x, where a, b, c, d, e are independent of x. Then, the value of e isA. 4B. 0C. 1D. none of these
Answer» Correct Answer - B Clearly, e is the value of L.H.S. of the given identity at x = 0 For x = 0, We obtain `LHS = \|(0,-1,3),(1,0,-4),(-3,4,0)\|` Note 1 Only square matrices have determinants. The matrices which are not square do not have determinants Note2 The determinant of a square matrix of order 3 can be expanded along any row or column. Note 3 If a row or a column of a determinant consists of all zeros, then the value of the determinant is zero. To evaluate the determinant of a square matrix of order 4 or more we follow the same procedure as discussed in evaluating the determinant of a square matrix of order 3.