Linear Algebra - Study Mode
[#76] Let M 4 = $$I$$, (where $$I$$ denotes the identity matrix) and M ≠ $$I$$, M 2 ≠ $$I$$ and M 3 ≠ $$I$$. Then, for any natural number k, M -1 equals:
Correct Answer
(C) M 4k + 3
[#77] The matrix [{ ext{A}} = left[ {x08egin{array}{*{20}{c}}
{frac{3}{2}}&0&{frac{1}{2}} \
0&{ - 1}&0 \
{frac{1}{2}}&0&{frac{3}{2}}
end{array}}
ight]] xa0 has three distinct eigen values and one of its eigen vectors is [left[ {x08egin{array}{*{20}{c}}
1 \
0 \
1
end{array}}
ight].] Which one of the following can be another eigen vector of A?
Correct Answer
(C) [left[ {x08egin{array}{*{20}{c}}
1 \
0 \
{ - 1}
end{array}}
ight]]
[#78] The determinant [left| {x08egin{array}{*{20}{c}}
{1 + { ext{b}}}&{ ext{b}}&1 \
{ ext{b}}&{1 + { ext{b}}}&1 \
2&{2{ ext{b}}}&1
end{array}}
ight|] xa0 xa0equals to
Correct Answer
(A) 0
[#79] The solution of the system of equations x + y + z = 4, x - y + z = 0, 2x + y + z = 5 is
Correct Answer
(D) x = 1, y = 2, z = 1
[#80] Which one of the following is an eigen vector of the matrix [left[ {x08egin{array}{*{20}{c}}
5&0&0&0 \
0&5&5&0 \
0&0&2&1 \
0&0&3&1
end{array}}
ight]?]
Correct Answer
(A) [left[ {x08egin{array}{*{20}{c}}
1 \
{ - 2} \
0 \
0
end{array}}
ight]]