Linear Algebra - Study Mode
[#141] If A is square symmetrical real valued matrix of dimensions 2n, then eigen values of A are
Correct Answer
(B) 2n real values not necessarily distinct
[#142] The eigen values of the matrix given below are [left[ {x08egin{array}{*{20}{c}}
0&1&0 \
0&0&1 \
0&{ - 3}&{ - 4}
end{array}}
ight]]
Correct Answer
(A) (0, -1, -3)
[#143] [{ ext{P}} = {left[ {x08egin{array}{*{20}{c}}
{ - 10} \
{ - 1} \
3
end{array}}
ight]^{ ext{T}}},{ ext{Q}} = {left[ {x08egin{array}{*{20}{c}}
{ - 2} \
{ - 5} \
9
end{array}}
ight]^{ ext{T}}}] xa0 xa0 and [{ ext{R}} = {left[ {x08egin{array}{*{20}{c}}
2 \
{ - 7} \
{12}
end{array}}
ight]^{ ext{T}}}] xa0are three vectors. An orthogonal set of vectors having a span that contains P, Q, R is
Correct Answer
(A) [left[ {x08egin{array}{*{20}{c}}
{ - 6} \
{ - 3} \
6
end{array}}
ight]left[ {x08egin{array}{*{20}{c}}
4 \
{ - 2} \
3
end{array}}
ight]]
[#144] The eigen values of the matrix [left[ {x08egin{array}{*{20}{c}}
4&{ - 2} \
{ - 2}&1
end{array}}
ight]]
Correct Answer
(C) are 0 and 5
[#145] For the set of equations x 1 + 2x 2 + x 3 + 4x 4 = 2 3x 1 + 6x 2 + 3x 3 + 12x 4 = 6 the following statement is true:
Correct Answer
(D) Multiple non-trivial solutions exist