Let M be
-15 -4
M =
Then, given that the superscript T stands for the transpose, after diagonalization, the matrix of the linear transformation corresponding to M is 0 after diagonalization, the matrix of the linear transformation corresponding to M is Lo the eigenvalues of M are -1 and -2, with eigenvectors (5 1)T and (3 1)T the eigenvalues of M are 1 and 2, with eigenvectors (3/2 1)T and (3/2 1)T the eigenvalues of M are 1 and 2, with eigenvectors (5/2 1)T and (3 1)T , respectively
The determinant of a matrix is equal to the sum of its pivots the product of its pivots the sum of its diagonal entries the product of its diagonal entries None of the above
10 Let
A = Lo 33 J;
e1 = (1 0)T and e2 = (0 1)T , in which the superscript T stands for the transpose Then, A applied on e1 shrinks it by a factor of 2 applied on e2 shrinks it by a factor of 3 A applied on (e1 + e2) stretches it by a factor of 2 in the direction of e1 and shrinks it by a factor of 3 in the direction of e2 A applied on (e1 + e2) stretches it by a factor of 2 in the direction of e1 and stretches it by a factor of 3 in the direction of e2 none of the above