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