Linear Algebra - Study Mode
[#116] Fora given matrix [{ ext{A}} = left[ {x08egin{array}{*{20}{c}}
2&{ - 2}&3 \
{ - 2}&{ - 1}&6 \
1&2&0
end{array}}
ight],] xa0 xa0 one of the eigen values is 3. The other two eigen values are
Correct Answer
(B) 3, -5
[#117] Let A be n × n real valued square symmetric matrix of rank 2 with [sumlimits_{{ ext{i}} = 1}^{ ext{n}} {sumlimits_{{ ext{j}} = 1}^{ ext{n}} {{ ext{A}}_{{ ext{ij}}}^2} } = 50.] xa0 xa0Consider the following statements. I. One eigen value must be in [-5, 5] II. The eigen value with the largest magnitude must be strictly greater than 5. Which of the above statements about eigen values of A is/are necessarily CORRECT?
Correct Answer
(B) I only
[#118] Real matrices [A] 3×1 , [B] 3×3 , [C] 3×5 , [D] 5×3 , [E] 5×5 and [F] 5×1 are given. Matrices [B] and [E] are symmetric. Following statements are made with respect to these matrices. 1. Matrix product [F] T [C] T [B] [C] [F] is a scalar. 2. Matrix product [D] T [F] [D] is always symmetric. With reference to above statements, which of the following applies?
Correct Answer
(A) Statement 1 is true but 2 is false
[#119] Let the Eigen vector of the matrix [left[ {x08egin{array}{*{20}{c}}
1&2 \
0&2
end{array}}
ight]] xa0be written in the form [left[ {x08egin{array}{*{20}{c}}
1 \
{ ext{a}}
end{array}}
ight]] and [left[ {x08egin{array}{*{20}{c}}
1 \
{ ext{b}}
end{array}}
ight]]. What is the value of (a + b) = ?
Correct Answer
(B) [frac{1}{2}]
[#120] Which one of the following matrices is singular?
Correct Answer
(C) [left[ {x08egin{array}{*{20}{c}}
2&4 \
3&6
end{array}}
ight]]