(1 point) Find all possible values of a, if any, for which the matrix 6-2 0...
(1 point) Let A = -3 -1 6 -4 0 6 -2 -1 5 If possible, find an invertible matrix P so that D = P-1 AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P= D= Is A diagonalizable over R? choose Be sure you can explain why or why...
(1 point) Given the matrix a 4 6 find all values of a that make = 0 . Give your answer as a comma-separated list. Values of a:
2. Consider the matrix 11 2 4 0 0 -1 1 7 0 0 0 6 10 007) Is this matrix diagonalizable? Explain why or why not. 3. Consider the matrix /1 a b 5 0 1 C 3 A = 0 0 1 2 0 0 0 2 For which values of a, b, c E R is A diagonalizable? Justify your answer.
(1 point) Let -9 -1 10 A = -4 2 -7 -1 If possible, find an invertible matrix P so that D = P-AP is a diagonal matrix. If it is not possible, enter the identity matrix for Pand the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P = D = Is A diagonalizable over R? diagonalizable Be sure you can explain why or why not.
(1 point) Let 3 -4 A = -4 -1 -4 -2 -2 If possible, find an invertible matrix P so that D = P-1 AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P= II II D= Be sure you can explain why or why Is A diagonalizable over R? diagonalizable...
Find all the values of k for which the following matrix is invertible [k-1 k-1 0 k2 2 k 0 k-1 k-1
1 . ] 8. Systems of differential equations. To 1 0 1. Find the eigen values and corresponding eigen spaces for the matrix A= 0 0 1 L32 0 -6 2. Use your answer from part 8.1 to determine if A is diagonalizable. 3. Find the Jordan normal form of A. Justify your answer. Hint: look at the possible Jordan forms for the matrix A first. 4. Verify that A= PJP-1, where 1-4 1 0 1 J= 0 -40 and...
Answer 7,8,9
1-11-1)--[-13.-(41-44)--:-- 3 1 0 0 -1 0 5 4 2-3 0 0 0 6. Consider the matrix A, above. Use diagonalization to evaluate A. 7. Consider the matrix B, above. Find a diagonal matrix D, and invertible matrix P, such that BPDP-1 8. Consider the matrix C, above. Find a diagonal matrix D, and invertible matrix P, such that C = PDP-1. If this is not possible, thus the matrix is not diagonalizable, explain why. 9. Consider the...
[2 pointsLet A= a b 3 20 620 6 Find all possible values of a and b for which A is a symmetric matrix. [3 points] Fill in the blanks with MIGHT, CANNOT, or MUST. Give a brief explanation of your answer. (a) If the columns of A are linearly independent, then AX = B have a unique solution. (b) If A is a square matrix and AX =B has only the trivial solution, then det(A) equal 0. form a...
Consider the following matrix 2 0 OY A= 1 2 10 24/ a Does A has an inverse? Why or why not? b. Is A diagonalizable? c. IfA is diagonalizable, find the matrix P that diagonalizes A. d. For your P, what is the diagonal matrix D? (DO NOT find P-1.just write down D) Write down the fundamental solution matrix (t) for the system of ODEs. /2 0 0 1 2X 0 24/ OV X'=