SOLUTION: consider the matrix p (t+2 3t t+1)
0 t-1 0
2t+4 t 3t+1
where t is a real number
evaluate the determinant of p in term of t
fo
Algebra ->
Matrices-and-determiminant
-> SOLUTION: consider the matrix p (t+2 3t t+1)
0 t-1 0
2t+4 t 3t+1
where t is a real number
evaluate the determinant of p in term of t
fo
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Question 1148590: consider the matrix p (t+2 3t t+1)
0 t-1 0
2t+4 t 3t+1
where t is a real number
evaluate the determinant of p in term of t
for what value or values of t does matrix p has zero as its determinant Answer by ikleyn(52803) (Show Source):
The matrix is
P =
If you write all 6 the determinant's terms, 4 of them (out-the-diagonals-terms) will contain 0 (zero) as a factor,
and, therefore, will be equal to zero.
The only two diagonal terms will contribute to the determinant
det(P) = (t+2)*(t-1)*(3t+1) - (2t+4)*(t-1)*(t+1) = (t-1)*((t+2)*(3t+1) - (2t+4)*(t+1)) =
= (t-1)*(t+2)*((3t+1) - 2*(t+1)) = (t-1)*(t+2)*(t-1) = (t+2)*(t-1)^2.
The zeroes of the determinant are the values t= -2 (of multiplicity 1) and t= 1 (of multiplicity 2).
