# Linear Algebra · Engineering Mathematics · GATE ECE

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GATE ECE 2022
Consider a system of linear equations Ax = b, where $$A = \left[ {\matrix{ 1 \hfill & { - \sqrt 2 } \hfill & 3 \hfill \cr { - 1} \hfill & {\sq... GATE ECE 2022 Let$$\alpha$$,$$\beta$$two non-zero real numbers and v1, v2 be two non-zero real vectors of size 3$$\times$$1. Suppose that v1 and v2 satisfy$$v...
GATE ECE 2018
Let M be a real 4 $$\times$$ 4 matrix. Consider the following statements : S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eige...
GATE ECE 2018
Consider matrix $$A = \left[ {\matrix{ k & {2k} \cr {{k^2} - k} & {{k^2}} \cr } } \right]$$ and vector $$X = \left[ {\matrix{ {... GATE ECE 2017 Set 1 The rank of the matrix$$M = \left[ {\matrix{ 5 & {10} & {10} \cr 1 & 0 & 2 \cr 3 & 6 & 6 \cr } } \right]$$i... GATE ECE 2017 Set 1 Consider the$$5 \times 5$$matrix$$A = \left[ {\matrix{ 1 & 2 & 3 & 4 & 5 \cr 5 & 1 & 2 & 3 & 4 \cr 4 &...
GATE ECE 2016 Set 3
Consider a $$2 \times 2$$ square matrix $$A = \left[ {\matrix{ \sigma & x \cr \omega & \sigma \cr } } \right]$$ Where $$x$$ is ...
GATE ECE 2016 Set 2
The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 9 & 7 & {13} \cr { - 6} & { - 4} & {... GATE ECE 2016 Set 1 Let$${M^4} = {\rm I}$$(where$${\rm I}$$denotes the identity matrix) and$$M \ne {\rm I},\,\,{M^2} \ne {\rm I}$$and$${M^3} \ne {\rm I}$$. Then, ... GATE ECE 2015 Set 3 For$$A = \left[ {\matrix{ 1 & {\tan x} \cr { - \tan x} & 1 \cr } } \right],$$the determinant of$${A^T}\,{A^{ - 1}}$$is GATE ECE 2015 Set 2 The value of$$'x'$$for which all the eigenvalues of the matrix given below are real is$$\left[ {\matrix{ {10} & {5 + j} & 4 \cr x ...
GATE ECE 2015 Set 1
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