DETAILS LARLINALG8 7.1.009. Determine whether x is an eigenvector of A. A= 6 2 2 3...
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x, y) = (x + h. y + k), h + 0 or k + 0 (translation in R2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.) 11
DETAILS LARLINALG8 1.R.004. Determine whether the equation is linear in the variables x and y. e-2x + 5y = 8 The equation is linear in the variables x and y. The equation is not linear in the variables x and y.
DETAILS LARLINALG8 7.3.033. Show that any two eigenvectors of the symmetric matrix A corresponding to distinct eigenvalues are orthogonal. 3 A = Find the characteristic polynomial of A. |u-A=1 Find the eigenvalues of A. (Enter your answers from smallest to largest.) (14, 12) = Find the general form for every eigenvector corresponding to 1. (Use s as your parameter.) X1 = Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) X2 = Find x,...
DETAILS LARLINALG8 8.4.013. Determine whether S is a basis for c2. S = = {(1, -i), (i, 1)) Sis a basis for c2 S is not a basis for c2
DETAILS LARLINALG8 3.R.027. Find JAl and A-11. 1 0 -2 А 0 3 = 2 - 5 7 6 (a) JA (b) |A-1,
ASK YOUR TEACHER DETAILS LARLINALG8 7.2.023. Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has a distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. Find the eigenvalues. (Enter your answers...
DETAILS LARLINALG8 6.R.030. Rotate the triangle with vertices (2, 3), (3, 2), and (2, 0) counterclockwise 90° about the point (3, 2). Graph the triangles. у y 10- 10+ 8 8 6 6 2 2 x X X 2 6 8 10 8 10 у 10 10 8 8 6 6 4 2 2 2 4 6 8 10 2 6 8 10
DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all that apply.) W = {f: f(0) = -1}, V = C[-1, 1] W is a subspace of V. W is not a subspace of V because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication.
DETAILS LARLINALG8 3.1.021. Use expansion by cofactors to find the determinant of the matrix. 6 6 1 04 3 0 0-3
plz solve all 3
9. (1/5 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.1.025. Find the characteristic equation and the eigenvalues and corresponding eigenvectors) of the matrix. 0 -3 -4 4 -6 0 0 (a) the characteristic equation (-23 +812 - 42 - 48) X (b) the eigenvalues (Enter your answers from smallest to largest.) (dzo dz, dz) = (-2,4,6 the corresponding eigenvectors Need Help? Read It Talk to a Tutor Submit Answer 10. [-/1 Points] DETAILS LARLINALG8 7.1.041. Find the eigenvalues...