i need help qith these i kind ofmwaited till the last second

i need help qith these, i kind ofmwaited till the last second so a quick response would be great. its a differentia\' equations problem

1. (4 points) Find the determinant of the matrix A, and determine all solutions x to the matrix equation Ax = 0. 4 -1 0 2. (6 points) Find the eigenvalues and eigenvectors of the matrix A given in question (1

Solution

|A| = 7(15)=105 (by expanding by iii row)

Now solving for Ax =0

As such trivial solution only exists as determinant not equals 0

Hence x=0, y =0 and z=0 is the only possible solution.

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A-lembda I =0 gives

eigen values as 7, 5, 3

Eigen vectors are (1,3,0)^T, ( 1,-1,0)^T (1,1,0)^T