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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

System of equations x + y = 2, 2x + 2y = 3 has ______ - Mathematics and Statistics

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प्रश्न

System of equations x + y = 2, 2x + 2y = 3 has ______

पर्याय

  • no solution

  • only one solution

  • many finite solutions.

  • infinite solutions.

MCQ
रिकाम्या जागा भरा
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उत्तर

no solution

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पाठ 1.2: Matrics - MCQ

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Solve the system of linear equations using the matrix method.

2x – y = –2

3x + 4y = 3


Solve the system of linear equations using the matrix method.

2x + 3y + 3z = 5

x − 2y + z = −4

3x − y − 2z = 3


Evaluate the following determinant:

\[\begin{vmatrix}x & - 7 \\ x & 5x + 1\end{vmatrix}\]


Evaluate the following determinant:

\[\begin{vmatrix}\cos \theta & - \sin \theta \\ \sin \theta & \cos \theta\end{vmatrix}\]


Evaluate
\[∆ = \begin{vmatrix}0 & \sin \alpha & - \cos \alpha \\ - \sin \alpha & 0 & \sin \beta \\ \cos \alpha & - \sin \beta & 0\end{vmatrix}\]


\[∆ = \begin{vmatrix}\cos \alpha \cos \beta & \cos \alpha \sin \beta & - \sin \alpha \\ - \sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{vmatrix}\]


Evaluate the following:

\[\begin{vmatrix}a + x & y & z \\ x & a + y & z \\ x & y & a + z\end{vmatrix}\]


\[\begin{vmatrix}1 + a & 1 & 1 \\ 1 & 1 + a & a \\ 1 & 1 & 1 + a\end{vmatrix} = a^3 + 3 a^2\]


​Solve the following determinant equation:

\[\begin{vmatrix}x + a & b & c \\ a & x + b & c \\ a & b & x + c\end{vmatrix} = 0\]

 


​Solve the following determinant equation:
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If \[\begin{vmatrix}a & b - y & c - z \\ a - x & b & c - z \\ a - x & b - y & c\end{vmatrix} =\] 0, then using properties of determinants, find the value of  \[\frac{a}{x} + \frac{b}{y} + \frac{c}{z}\]  , where \[x, y, z \neq\] 0


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Using determinants show that the following points are collinear:

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Using determinants prove that the points (ab), (a', b') and (a − a', b − b') are collinear if ab' = a'b.

 

If the points (3, −2), (x, 2), (8, 8) are collinear, find x using determinant.


Prove that :

\[\begin{vmatrix}1 & b + c & b^2 + c^2 \\ 1 & c + a & c^2 + a^2 \\ 1 & a + b & a^2 + b^2\end{vmatrix} = \left( a - b \right) \left( b - c \right) \left( c - a \right)\]

 


Prove that :

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9x + 5y = 10
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x − y + 3z = 6
x + 3y − 3z = − 4
5x + 3y + 3z = 10


Solve each of the following system of homogeneous linear equations.
x + y − 2z = 0
2x + y − 3z = 0
5x + 4y − 9z = 0


Solve each of the following system of homogeneous linear equations.
2x + 3y + 4z = 0
x + y + z = 0
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Find the value of the determinant 
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If \[A = \begin{bmatrix}1 & 2 \\ 3 & - 1\end{bmatrix}\text{ and B} = \begin{bmatrix}1 & - 4 \\ 3 & - 2\end{bmatrix},\text{ find }|AB|\]


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Find the maximum value of \[\begin{vmatrix}1 & 1 & 1 \\ 1 & 1 + \sin \theta & 1 \\ 1 & 1 & 1 + \cos \theta\end{vmatrix}\]


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6x − 12y + 25z = 4
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2x + 18y + 15z = 10


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 2x + 6y = 2
3x − z = −8
2x − y + z = −3


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 8x + 4y + 3z = 18
2x + y +z = 5
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x − y + 2z = 7
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