Orthogonally diagonalize A as PDPT A = O a. 1 V2 2 P= 0-102 2 2 b. 12 P = o=[6] -4 0 06 √ √2 OC. 2 V2 -60 P= D = 0 4 2 V2 002-[17] -[8] D- [8 ] Oe. P = 2 V2 Of. 2 2 P= p=[6 -] 1 1 2 2
Orthogonally diagonalize as
a.
b.
c.
d.
e.
f.
Orthogonally diagonalize A as PDPT A = ['$ ] a. 1 2 P = 1 2 1 2 D [ 6 0 0-4 1 2 b . Р = 1 1 2 12 1 1 2 2 D = 16] -60 04 - C. 2 2 P= D = 0-4 6 0 2 12 *-=[17] --66--] 0-60] O e. 1 2 v2 P = 2 12 O f. 1 2 Sila...
Orthogonally diagonalize A as PDPT A = 1 5 51
linear algebra 2 parts
part a
part b
А PDPT Orthogonally diagonalize as A = 1 22 1 1 V2 V2 -- P- 0-[8] b. 1 1 2 P- 0-16] 1 1 V2V P- 1 1 12 2 1 √2/2 0-168] 1 d. P 1 1 V2 V2 1 1 √ √ 0-16] e. p=[17] -=[:-] f. 1 P= 1 2 2 1 1 2 2 0-[• -] Solve the system 5 = ;3x - ܕܠ ܐ2 + X1 13...
(7') Orthogonally diagonalize the matrix (4 12). 1
1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2
1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. Enter the matrices P and D below. 1 1 (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Diagonalize
a.
b.
c.
d.
e.
f.
Diagonalize A A = 1 3 4 2 a. A = PDP-1 b. A = PDP-1 1 Р 1 1 OC. A = PDP-1 -1 3 P = 2 5 d. A = PDP-1 -3 1 P= -4 1 e. A = PDP-1 1 -1 P 3 1 Of A = PDP-1 P-[31] -- [6-2] [37] - [64] P=[ +3 z] --[: = D = 10 03
7. Orthogonally diagonalize the matrices by finding an orthogonal matrix Q and a diagonal matrix D such that QT AQ = D. 1 А 0 -1 0 0 -1 0 1 В = 2 0 0 1 0 1 0 0 0 0 1 0 1 0 0 2
Please write every step done, the gram-Schmidt process I
cannot understand
6. Orthogonally diagonalize each of the following symmetric matrices. Give the similarity transformation. 112] (b) 11 2 1 -8 1 3 7. Orthogonally diagonalize each of the following symmetric matrices. Give the similarity transformation. 1 31 L3 9 1.5-0.5 -0.5 1.5