Linear Algebra - Study Mode

[#96] If the system 2x - y + 3z = 2 x + y + 2z = 2 5x - y + az = b has infinitely many solutions, then the values of a and b, respectively, are
Correct Answer

(B) 8 and 6

[#97] For the matrix [{ ext{A}} = left[ {x08egin{array}{*{20}{c}}
3&{ - 2}&2 \
0&{ - 2}&1 \
0&0&1
end{array}}
ight],] xa0 xa0one of the eigen values is equal to -2. Which of the following is an eigen vector?
Correct Answer

(D) [left[ {x08egin{array}{*{20}{c}} 2 \ 5 \ 0 end{array}} ight]]

[#98] What are the eigen values of the following 2 × 2 matrix? [left[ {x08egin{array}{*{20}{c}}
2&{ - 1} \
{ - 4}&5
end{array}}
ight]]
Correct Answer

(B) 1 and 6

[#99] Eigen values of the matrix [left[ {x08egin{array}{*{20}{c}}
3&{ - 1}&{ - 1} \
{ - 1}&3&{ - 1} \
{ - 1}&{ - 1}&3
end{array}}
ight]] xa0 are
Correct Answer

(C) 1, 4, 4

[#100] If [{ ext{A}} = left[ {x08egin{array}{*{20}{c}}
1&5 \
6&2
end{array}}
ight]] xa0 and [{ ext{B}} = left[ {x08egin{array}{*{20}{c}}
3&7 \
8&4
end{array}}
ight],,{ ext{A}}{{ ext{B}}^{ ext{T}}}] xa0 xa0is equal to
Correct Answer

(A) [left[ {x08egin{array}{*{20}{c}} {38}&{28} \ {32}&{56} end{array}} ight]]