1
GATE CSE 2021 Set 1
Numerical
+2
-0
Consider the following matrix.
$$\left( {\begin{array}{*{20}{c}} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{array}} \right)$$
The largest eigenvalue of the above matrix is ______
Your input ____
2
GATE CSE 2020
MCQ (Single Correct Answer)
+2
-0.67
Let A and B be two n$$ \times $$n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements,
I. rank(AB) = rank(A) rank(B)
II. det(AB) = det(A) det(B)
III. rank(A + B) $$ \le $$ rank(A) + rank(B)
IV. det(A + B) $$ \le $$ det(A) + det(B)
Which of the above statements are TRUE?
I. rank(AB) = rank(A) rank(B)
II. det(AB) = det(A) det(B)
III. rank(A + B) $$ \le $$ rank(A) + rank(B)
IV. det(A + B) $$ \le $$ det(A) + det(B)
Which of the above statements are TRUE?
3
GATE CSE 2019
Numerical
+2
-0
Consider the following matrix :
$$ R=\left[\begin{array}{cccc} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{array}\right] $$
The absolute value of the product of Eigen values of $R$ is ___________.
Your input ____
4
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
Consider a matrix P whose only eigenvectors are the multiples of $$\left[ {\matrix{
1 \cr
4 \cr
} } \right].$$
Consider the following statements.
$$\left( {\rm I} \right)$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$P$$ does not have an inverse
$$\left( {\rm II} \right)$$ $$\,\,\,\,\,\,\,\,\,\,\,$$ $$P$$ has a repeated eigenvalue
$$\left( {\rm III} \right)$$ $$\,\,\,\,\,\,\,\,\,$$ $$P$$ cannot be diagonalized
Which one of the following options is correct?
Questions Asked from Linear Algebra (Marks 2)
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