Eigenvalues and Determinants in Matrices

Values that make the determinant of a matrix zero

Values that make the matrix invertible

Values that are solutions to a matrix equation

Values that are the sum of matrix elements

Finding the inverse of the matrix

Subtracting the identity matrix from the given matrix

Adding the identity matrix to the given matrix

Setting up the determinant equation

It is used to scale the matrix

It is subtracted from the given matrix

It is added to the given matrix

It is multiplied by lambda

By adding all terms

By multiplying and combining like terms

By dividing by lambda

By subtracting all terms

-180

180

-1638

1638

Finding the inverse of the matrix

Factoring the quadratic equation

Adding the identity matrix

Subtracting lambda

Lambda plus three and lambda minus six

Lambda minus six and lambda plus three

Lambda plus six and lambda minus three

Lambda and lambda

6

3

-3

-6

6

-6

3

-3

They determine the matrix's invertibility

They are used to calculate the matrix's trace

They help in solving linear equations

They provide insights into the matrix's properties