consider the system of linear equations eqalign and x1 2x2

Consider the system of linear equations;
$$\eqalign{ & {x_1} + 2{x_2} + {x_3} = 3 \cr & 2{x_1} + 3{x_2} + {x_3} = 3 \cr & 3{x_1} + 5{x_2} + 2{x_3} = 1 \cr} $$
The system has

A. exactly 3 solutions

B. a unique solution

C. no solution

D. infinite number of solutions

Answer : no solution

Solution :
\[D = \left| \begin{array}{l} 1\,\,\,\,\,\,\,2\,\,\,\,\,\,1\\ 2\,\,\,\,\,\,3\,\,\,\,\,\,1\\ 3\,\,\,\,\,\,5\,\,\,\,\,\,2 \end{array} \right| = 0\,\,\,\,\,\,\,{D_1} = \left| \begin{array}{l} 3\,\,\,\,\,\,2\,\,\,\,\,\,1\\ 3\,\,\,\,\,\,3\,\,\,\,\,\,1\\ 1\,\,\,\,\,\,5\,\,\,\,\,\,2 \end{array} \right| \ne 0\]
⇒ Given system, does not have any solution.
⇒ No solution

Releted MCQ Question on
Algebra >> Matrices and Determinants

Releted Question 1

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

A. $$C$$ is empty

B. $$B$$ has as many elements as $$C$$

C. $$A = B \cup C$$

D. $$B$$ has twice as many elements as elements as $$C$$

View Answer

Releted Question 2

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

A. 0

B. 1

C. $$i$$

D. $$\omega $$

View Answer

Releted Question 3

Let $$a, b, c$$ be the real numbers. Then following system of equations in $$x, y$$ and $$z$$
$$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - \frac{{{z^2}}}{{{c^2}}} = 1,$$ $$\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1,$$ $$ - \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1$$ has

A. no solution

B. unique solution

C. infinitely many solutions

D. finitely many solutions

View Answer

Releted Question 4

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

A. $$A + B = B + A$$

B. $$A + B = A - B$$

C. $$A - B = B - A$$

D. $$AB=BA$$

View Answer

Consider the system of linear equations;
$$\eqalign{ & {x_1} + 2{x_2} + {x_3} = 3 \cr & 2{x_1} + 3{x_2} + {x_3} = 3 \cr & 3{x_1} + 5{x_2} + 2{x_3} = 1 \cr} $$
The system has

Releted MCQ Question on
Algebra >> Matrices and Determinants

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

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Matrices and Determinants

Practice More MCQ Question on Maths Section

Consider the system of linear equations; $$\eqalign{ & {x_1} + 2{x_2} + {x_3} = 3 \cr & 2{x_1} + 3{x_2} + {x_3} = 3 \cr & 3{x_1} + 5{x_2} + 2{x_3} = 1 \cr} $$ The system has

Releted MCQ Question on Algebra >> Matrices and Determinants

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then \[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

Practice More Releted MCQ Question on Matrices and Determinants

Practice More MCQ Question on Maths Section

Consider the system of linear equations;
$$\eqalign{ & {x_1} + 2{x_2} + {x_3} = 3 \cr & 2{x_1} + 3{x_2} + {x_3} = 3 \cr & 3{x_1} + 5{x_2} + 2{x_3} = 1 \cr} $$
The system has

Releted MCQ Question on
Algebra >> Matrices and Determinants

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

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Matrices and Determinants