Question

1. Let A be a square matrix such that detal - A) = 112 - 6/11 + 9210 a.) (3 points) What is the size of A? b.) (4 points) Is A invertible? Why or why not? c.) (3 points) How many eigenspaces does A have?

Answer 1

0 Given (Al-Al 22 62 'tanto :. If the characteristic Equation is of ordin' the Matrix is of size Coxn) Geven characteristic Equation is of ordo 12 Size of Matrix A is [12x12] 6 from Given characteristic polynominal |A2Ako a'2 q altanloo No (a-bata] =o aka-3]*20 a 20,0,0,0,0,0,0,0,0,0,3,3 . Given matrix has figen Value of to matris A is not Invertible :: only of A square matrix is Invertible if and o is not Eigen Value Value

The Eigen Vectors conesponding to Eiger Valeo are called Eigen Spaces Matrix A hos dzo ire, to A has to Gigen spaces.
the answers for above questions are solved