am_knightmare said:Just solved it. thanks for the reply though.
1 1 1
a b c
a^2 b^2 c^2
becomes
1 0 0
a b-a c-a
a^2 (b^2-a^2) (c^2-a^2)
then becomes
(b-a)(c-a) times
1 0 0
a 1 1
a^2 b-a c-a
then
1 0 0
a 1 0
a^2 b-a c-b
det= 1 x 1 x(c-b) ( c-a) (b-a)
A matrix is a rectangular array of numbers or symbols arranged in rows and columns. It is used in mathematics and science to represent and manipulate data.
The determinant of a matrix is a value that can be calculated from the elements of the matrix. It is a measure of the matrix's size and orientation, and is used in many mathematical operations such as finding inverses and solving systems of equations.
There are multiple methods for finding the determinant of a matrix, but one common way is to use the properties of determinants. These properties include multiplying a row by a scalar, adding a multiple of one row to another row, and swapping two rows. By using these properties, the determinant can be simplified to a simpler form that is easier to calculate.
The determinant is important because it is used in many mathematical operations, such as finding inverses, solving systems of equations, and calculating volumes of parallelepipeds. It also has geometric interpretations, such as determining the orientation of a set of vectors in space.
Yes, the determinant of a matrix can be negative. This usually occurs when there is an odd number of row swaps during the calculation of the determinant. However, the sign of the determinant does not affect its value, and it is still considered a valid measure of the matrix's size and orientation.