linear algebra 2 parts
part a
part b
1)
Solution:
A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such that A=PDP-1
Here A | = |
|
Find eigenvalues of the matrix A
|A-λI|=0
|
= 0 |
∴(1-λ)×(1-λ)-5×5=0
∴(1-2λ+λ2)-25=0
∴(λ2-2λ-24)=0
∴(λ+4)(λ-6)=0
∴(λ+4)=0 or (λ-6)=0
∴ The eigenvalues of the matrix A are given by λ=-4,6,
1. Eigenvectors for λ=-4
v1= |
|
2. Eigenvectors for λ=6
v2= |
|
The eigenvectors compose the columns of matrix P
∴P | = |
|
The diagonal matrix D is composed of the eigenvalues
∴D | = |
|
hence option e is correct.
linear algebra 2 parts part a part b А PDPT Orthogonally diagonalize as A = 1...
linear algebra 2 parts mcq
part a
part b
Solve the system 5 = ;3x - ܕܠ ܐ2 + X1 13 = 3xa - ܕ2xn + X -X+ X2 ܂3 1 xto tec b. Xt tec SE N 51 0 d. XS ܢܬ ܝ ܝ SEC e X=S <. [ f. x=s H Let be the set of third degree polynomials H = {ax + ax? + ax | AEC} Is H a subspace of ? Why or why not?...
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 = 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 A as PDPT A = [5] O a. 1 P = 1 v2 V2 1 1 /2 √2 D = -[6-4) b. O 1 2 1 2 6 0 P= D = 1 1 0-4 2 2 1 2 12 P = D = = [ ] 0-4 6 0 1 v2 d. 1 1 12 P = 12 1 v2 0-19 1 Oe. 1 1 P= 2 12 1 (2 √2 D-[64] of p=[171] -- [6 -4]
linear algebra
part a
part b
Find N(A) A = 1 -3 4 -1 9 -2 6 -6 -1 -10 -39 -6 -6 -3 3-94 9 0 a. 6 N(A) = 4 -1 ୨ 10 E. N(A) = 0 3 2 ) 0 0 C T ୨ NA - -6 -1 -10. -] ୨ =5 - -] ୨ ) d, N(A) = 3 0 0 2 0 5 1 1 0 0 0 NA - 1 1 0 0 -2...
Solve the system
a.
b.
c.
d.
e.
f.
Solve the system X1 + 2x2 – 3x3 = 5 2x1 + x2 – 3x3 = 13 - X1 + X2 -8 2 X=S 3 SEC -5 a. b. 1 x=t0], tec x=s -1 SEC d. 1 x= t 1 tec 1 e. O 1 0 X=S SEC -1 0 o f. 1 SEC x=s 1 0
linear algebra 2 part mcq
part a
part b
r(A) Find and n(A) A = 1 - 3 4 -1 9 -2 6 -6 -1 -10 -39 -6 -6 -3 3 -94 9 0 a. r(A) = 5 n(A) = 0 b. r(A) = 3 n(A) = 2 c. (A) = 0 n(A) = 5 d. r(A) = 1 n(A) = 4 e. r(A) = 4 n(A) = 1 f. r(A) = 2 n(A) = 3 А Diagonalize A =...
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1. Let Xi l be a random sample from a normal distribution with mean μ 50 and...
This is linear algebra so please use the right formulas to solve
these problems. Thanks!
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2)
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