Soru
Use the appropriate property of determinants to find a. Do not evaluate the determinants. vert } 4&23&-3 -43&-31&-17 3&-3&9 vert Answer: a=
Çözüm
4.7
(311 Oylar)
İlayda
Elit · 8 yıl öğretmeni
Uzman doğrulaması
Cevap
To find the value of
, we can use the property of determinants that states that multiplying a row (or column) of a matrix by a scalar multiplies the determinant of the matrix by the same scalar.In this case, we have the determinant of a 3x3 matrix and we want to find the value of
such that the determinant of the matrix remains unchanged when the first row is multiplied by
.The given determinant is:
We want to find
such that:
Comparing the two determinants, we can see that the second determinant is obtained by multiplying the first row of the original determinant by
. Therefore, we have:
Since the determinants are equal, we have:
Solving for
, we get:
Therefore, the value of
is
.