SOLUTION: Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. [2 1 0] [0 -2 4] [0 1 -3]

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. [2 1 0] [0 -2 4] [0 1 -3]       Log On


   

Question 1129197: Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse.
[2 1 0]
[0 -2 4]
[0 1 -3]

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29

The determinant is:
D+=+a%28ei+-+fh%29+-b%28di+-+fg%29+%2B+c%28dh+-eg%29
matrix%283%2C3%2C2%2C+1%2C+0%2C%0D%0A0%2C+-2%2C+4%2C%0D%0A0+%2C1%2C+-3%29

D+=+2%286+-+4%29+-+1%280%2A0%29+%2B+0%280%29
D+=+2%282%29
D+=+4

the matrix
matrix%283%2C3%2C2%2C+1%2C+0%2C%0D%0A0%2C+-2%2C+4%2C%0D%0A0+%2C1%2C+-3%29 have inverse because D = 4
If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
If you need to learn about the determinant of a 3x3-matrix, read the lesson
    - Determinant of a 3x3 matrix
    - Co-factoring the determinant of a 3x3 matrix
in this site.