Question

T3. The French mathematician Jacques Hadamard (1865–1963) proved that if A is an n x n matrix each of whose entries satisfies the condition lajj| < M, then det(A) < Vn"M" (Hadamard's inequality). For the following matrix A, use this re- sult to find an interval of possible values for det(A), and then use your technology utility to show that the value of det(A) falls within this interval. 50.3 -2.4 -1.7 2.57 [0.2 -0.3 -1.2 1.4 |2.5 2.3 0.0 1.8 L1.7 1.0 -2.1 2.3. A=

Answer 1

Answer Given 10.3 -2.4 -1.4 2.57 A = 0.2 -0.3 -1.2 1.4 2.5 2.3 0.0 1.8 117 1.0 -2.1 2.3 clearly A is a 4 columes and 4 rows 4x4 Matrix Also l oil 52.5 Isi; js4 - loet Al Eſ 44 (2.5)4 16 x 39.0625 = 625 13 -24 IAL - To 14 12 3 -17 257 -12 14 TAL- 25 Lii 23 10 0 -21 18 23 - 18656 = -7.8656

you can do in the following way Attivst eliminate then I colonn under the ist element : 13 -24 17 25 1 Tale - O 13 -703 -8/3 To 223 -4273 -5743 To 146 +352/3 -356/3 . After that max a elements zero in and coloum aften und element After that make it diagonal. 13 -24 17 25 TAJ = tolo 13 - #013 - 8/9 10085/39 -5639739 lo 0 0 -78656 6008 Multiply the diagonal element and get ial