1.) 2.) 3.) 4.) 5.) 6.) 7.) 8.) 9.) 10.) 11.)

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11 Linear Algebra Problems


1.) 2.) 3.) 4.) 5.) 6.) 7.) 8.) 9.) 10.) 11.)
Answered Same DayMay 13, 2021

Answer To: 1.) 2.) 3.) 4.) 5.) 6.) 7.) 8.) 9.) 10.) 11.)

Rajeswari answered on May 14 2021
136 Votes
1.)
a) u-2v = (1,2,-1)-2(1,0,3) = (-1, 2, -7)
||u-2v|| +w =
b) u.v = 1+0-3 = -2
c) uxv = =i(6)-
j(3+1)+k(-2) = 6i-4j-2k
d) If u.w is negative then angle is obtuse. U.w = 1+6-5 >0 hence angle is acute
e) Orthogonal to u and v is uxv
Unit vector =
2.)
u.v = -2+6+0-4 =0
Orthogonal.
U+v = (-1,5,1,3)
||u+v||2 = 1+25+1+9 = 36
||u||2=4+9+1+16 = 30
||v||2=1+4+0+1 = 6
We find that sum of squares equals square of sum.
Hence u and v satisfy Pythagorean theorem.
3.)
We know that axa =0 and also cross product is distributive.
Hence (mu +kv)xv = m(uXv) +k(vxv) . But vxv =0
Hence we get
(mu +kv)xv = m(uxv) = uxmv
4.)
a) u.(wxv) = -u.(vxw) = +5
b) (wxv).u = -(-5) = 5
c) U.(vxv) = u.0 =...
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