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Let E be the matrix given by -3 E= -12 -1 -1] 0 5 -2 -1] Determine if E is diagonalizable. If it is, find a basis of C consis
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-- 3 0 5 sol @ To Find use is diagonalizable. D, P-AP (gt Ps stalishes this, then 81 is Dragonalizable Eigen values for it NoVo 8:01 PM 0.OKB/s na 51 Х Eigenvalues and Eigenv... https://matrixcalc.org Clean 1. Find eigenvalues from the characteristic8:01 PM 0.6KB/s Vo LTE 51 1 1.11--2 2. 12 = -2 * V5 - 1 3.13 = 2 V5 - 1 2. For every 2 we find its own vector(s): 1. 11 = -2Vo 8:01 PM 7.8KB/s na 51 ? 1 1 0 R1/(-1) - R1 1 1 8) x(12) 2 -50 -12 4 -2 1 = ? R2-(-12) *R1 - R2 1 1 10 0 14 70 4 -2 10 *(-4Vo 8:02 PM 1.1KB/s 51 ? R2/(14) - R 2 1 1 0 (1 1 o x(6) 0 -6 -30 ? *R 2 R3 R3 -(-6) 1 1 1 0 1 *(-1) 0 (1 0 0 0 0 1 1 0 0 ? 2Vo 8:02 PM 0.0KB/s 51 = Find the variable x2 from the equation 2 of the system (1): x2 = {xx3 2 • Find the variable x, from tVo 8:02 PM 0.0KB/s QA 51 -1 xX3 2. General Solution 2:X=11xx3 2. X 3 = 2. -1 The solution set: X3 * 2. 1 2. Let x 3 = 1, V1=8:02 PM 0.1KB/s na Vo LTE 51 Αν = λν (A - 21)v = 0 So we have a homogeneous system of linear equations, we solve it by GaussiVo 8:03 PM 35.4KB/s 02 51 ? 0 R3-4×R → R3 -5 - 1 -V5 - 1 1 8 8. V5 - 1 -3 × V5 - 13 0 2 2. 5 - 3 5 x V5 + 1 2. 2. V5 + 1) 0 x8:03 PM 75.2KB/s na Vo LTE 51 15 - 3 R3 - 2 -V5 - 1 1 xR2 - R3 -V5 - 1 0 8 -4* V5 - 70 0 0 (15 + 1 8 1-15 0 1 0 0 ? R (**)* RVo 8:03 PM 1.3KB/s AA 51 • Find the variable x 2 from the equation 2 of the system (1): x2 = (4 * v5 + 7)*xg • Find the varia8:03 PM 1.2KB/s na Vo LTE 51 X X 3 General Solution 3 x V5 + 7 2 X= (4 x V5 + 7) * x3 X wo The solution set: 3 x 15 + 7 2 X38:03 PM 0.OKB/s na Vo LTE 51 Αν = λν (A - 21) v = 0 So we have a homogeneous system of linear equations, we solve it by GaussVo 8:03 PM 58.2KB/s 2 A 51 0 R2-(-12) Ⓡ R1 - R2 15 - 1 15 - 1 1 8 8 -V5 - 1 315 - 13 2 2 4. -2 -2 x 15 1 *(-4) o 0 0 ? R3-4*R8:03 PM 61.2KB/s 2 A Vo LTE 51 ?. R3 -(45= 3)* R2 - R$ 15 - 1 15 - 1 1 0 15 + 1 8 8 x 8 0 1 4x V5 - 70 0 0 0 0 E ? ~ R1-(* )8:03 PM 61.2KB/s 2 A Vo LTE 51 ?. R3 -(45= 3)* R2 - R$ 15 - 1 15 - 1 1 0 15 + 1 8 8 x 8 0 1 4x V5 - 70 0 0 0 0 E ? ~ R1-(* )Vo 8:03 PM 0.0KB/s 51 • Find the variable x2 from the equation 2 of the system (1): x2 = (-4x V5 + 7) * x3 • Find the variabl12 3V567 2 - 1/2 UV5+7 a 1 13 -3547 -u 5+1 2 14/19 16 19 -375 +8 8V5-15 19 95 31578-8V5-15 95 - 715725 190 -9V5715 715 +25 19Vo 8:11 PM 0.0KB/s 51 Insert in A Insert in B Clean V 3 x 15 + 7 (-1) -1 2 -1 - 3x √5 + 7 2 -34 35 2 = 4x V5 + 7 -4* V5 + 7 2

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