Linear Algebra - Study Mode

[#126] The rank of the matrix [left[ {x08egin{array}{*{20}{c}}
1&1&1 \
1&{ - 1}&0 \
1&1&1
end{array}}
ight]] xa0is
Correct Answer

(C) 2

[#127] It is given that X 1 , X 2 , ... X M are M non-zero, orthogonal vectors. The dimension of the vector space spanned by the 2M vectors X 1 , X 2 ... X M , -X 1 , -X 2 ... -X M is
Correct Answer

(C) M

[#128] Consider the set of (column) vectors defined by X = {x [ in ] R 3 | x 1 + x 2 + x 3 = 0, where x T =[x 1 , x 2 , x 3 ] T }. Which of the following is TRUE?
Correct Answer

(A) {[1, -1, 0] T , [1, 0, -1] T } is a basis for the subspace X

[#129] For given matrix [{ ext{P}} = left[ {x08egin{array}{*{20}{c}}
{4 + 3{ ext{i}}}&{ - { ext{i}}} \
{ ext{i}}&{4 - 3{ ext{i}}}
end{array}}
ight]] xa0 xa0where [{ ext{i}} = sqrt { - 1} ,] xa0 the inverse of matrix P is
Correct Answer

(A) [frac{1}{{24}}left[ {x08egin{array}{*{20}{c}} {4 - 3{ ext{i}}}&{ ext{i}} \ { - { ext{i}}}&{4 + 3{ ext{i}}} end{array}} ight]]

[#130] The matrix [left[ {x08egin{array}{*{20}{c}}
1&2&4 \
3&0&6 \
1&1&{ ext{p}}
end{array}}
ight]] xa0has one eigen value equal to 3. The sum of the other two eigen values is
Correct Answer

(C) p - 2