WebJul 7, 2024 · If 1 is an eigenvalue of A find eigenvalues for matrix A 2 − 2 I? In this question I got eigenvalues of A = 1, 1 + i, 1 − i . I was thinking to change λ to λ 2 − 2 in characteristic equation of A to get eigenvalues of required matrix. I m getting characteristic equation x 6 − 9 x 4 + 28 x 2 − 30 = 0. Let x = λ. Can anyone tell me why I m wrong? WebDec 21, 2024 · Best answer A = [ 1 2 −1 3] A = [ 1 2 - 1 3] ⇒ A2 = [ 1 2 −1 3][ 1 2 −1 3] = [ −1 8 −4 7] = 4A − 5I ⇒ A 2 = [ 1 2 - 1 3] [ 1 2 - 1 3] = [ - 1 8 - 4 7] = 4 A - 5 I ⇒ A3 = AA2 = A(4A − 5I) ⇒ A 3 = A A 2 = A ( 4 A - 5 I) = 4A2 − 5A = 4 A 2 - 5 A = 4(4A − 5I) − 5A = 4 ( 4 A - 5 I) - 5 A = 11A − 20I = 11 A - 20 I

Find k, if A = [3-24-2] and A2 = kA – 2I. - Shaalaa.com

WebMar 23, 2024 · Question 6 If A = [ 8 (3& [email protected] −1&2)] and I = [ 8 (1& [email protected] &1)], find k so that A2 = 5A + kI Finding A2 A2 = [ 8 (3& [email protected] −1&2)] [ 8 (3& [email protected] −1&2)] A2 = [ 8 (3 (3)+1 (−1)&3 (1)+1 (2)@−1 (3)+2 (−1)&−1 (1)+2 (2))] A2 = [ 8 (9−1& [email protected] −3−2&−1+4)] A2 = [ 8 (8& [email protected] −5&3)] … WebA 2 = k A − 2 I 2 ⇒ [ 1 − 2 4 − 4] = k [ 3 − 2 4 − 2] − 2 [ 1 0 0 1] ⇒ [ 1 − 2 4 − 4] = [ 3 k − 2 k 4 k − 2 k] − [ 2 0 0 2] ⇒ [ 1 − 2 4 − 4] = [ 3 k − 2 − 2 k − 0 4 k − 0 − 2 k − 2] The … cure chesty cough

If matrix \\[A=\\left[ \\begin{matrix}3 -2 \\\\4 -2 \\\\\\end{matrix ...

WebBy definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get. 3k−2 =1 ⇒k= 1 … WebA 2 = A.A . Now, A 2 = kA – 2I. Comparing the corresponding elements, we get, 3k -2 = 1. ⇒ 3k = 3. ⇒ k = 1. Therefore, the value of k is 1. WebConsider the matrix `A=[[3,-2],[4,-2]]` find k so that `A^2=kA-2I` Class 12 MATH Doubtnut - YouTube Consider the matrix `A=[[3,-2],[4,-2]]` find k so that `A^2=kA-2I`Welcome to... cure chick personalized plate