For the set of equations x1 + 2x2 + x3 +...

Home / Engineering Maths / Linear Algebra / Question

Examveda

For the set of equations
x₁ + 2x₂ + x₃ + 4x₄ = 2
3x₁ + 6x₂ + 3x₃ + 12x₄ = 6
the following statement is true:

A. Only the trivial solution x₁ = x₂ = x₃ = x₄ = 0 exists

B. There are no solution

C. A unique non-trivial solution exists

D. Multiple non-trivial solutions exist

Answer: Option D

This Question Belongs to Engineering Maths >> Linear Algebra

Join The Discussion

Related Questions on Linear Algebra

If $${\left[ {1,\,0,\, - 1} \right]^{\text{T}}}$$ is an eigen vector of the following matrix \[\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&0 \\ { - 1}&2&{ - 1} \\ 0&{ - 1}&1 \end{array}} \right]\] then corresponding eigen value is

A. 1

B. 2

C. 3

D. 5

View Answer

View Answer

The eigen values of the following matrix are \[\left[ {\begin{array}{*{20}{c}} { - 1}&3&5 \\ { - 3}&{ - 1}&6 \\ 0&0&3 \end{array}} \right]\]

A. 3, 3 + 5j, 6 - j

B. -6 + 5j, 3 + j, 3 - j

C. 3 + j, 3 - j, 5 + j

D. 3, -1 + 3j, -1 - 3j

View Answer

View Answer

Let A be the 2 × 2 matrix with elements a₁₁ = a₁₂ = a₂₁ = +1 and a₂₂ = -1. Then the eigen values of the matrix A¹⁹ are

A. 1024 and -1024

B. 1024√2 and -1024√2

C. 4√2 and -4√2

D. 512√2 and -512√2

View Answer

View Answer

How many of the following matrices have an eigen value 1?
\[\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 0&1 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 1&{ - 1} \\ 1&1 \end{array}} \right]{\text{ and }}\left[ {\begin{array}{*{20}{c}} { - 1}&0 \\ 1&{ - 1} \end{array}} \right]\]

A. one

B. two

C. three

D. four

View Answer

View Answer

More Related Questions on Linear Algebra