Using the properties of determinants, show that(a)a3 a2 1b3 b2 1c3 c2 1
Question
Using the properties of determinants, show that(a)a3 a2 1b3 b2 1c3 c2 1
Solution
The given matrix is:
| a³ a² 1 | | b³ b² 1 | | c³ c² 1 |
We can use the properties of determinants to simplify this.
Step 1: Subtract the second column from the first, and the third column from the second. This gives us:
| a³-a² a²-1 1 | | b³-b² b²-1 1 | | c³-c² c²-1 1 |
Step 2: Factor out a², b², and c² from the first and second columns:
| a²(a-1) a²(1-1/a) 1 | | b²(b-1) b²(1-1/b) 1 | | c²(c-1) c²(1-1/c) 1 |
Step 3: Now, we can see that the first two columns are proportional, so the determinant of this matrix is 0.
Therefore, the determinant of the original matrix is also 0.
Similar Questions
sing the properties of determinants, show thata + b a aa a + b aa a a + b= b2(3a + b)
Properties of Determinant of Matrix
give me 5 sums to solve to find determinants of a matrix
The determinant of an n×n matrix A is the product of the diagonal entries in A.A. TrueB. False
Suppose that A and B are n×n matrices. Check the true statements below: A. If det(A) is zero, then two rows or two columns are the same, or a row or a column is zero.B. det(AT)=(−1)det(A)C. If two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix.D. The determinant of A is the product of the diagonal entries in A
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.