Maths-
General
Easy
Question
The value of
for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution is
- 3
- -3
- 2
- -2
The correct answer is: -2
The question is as follows the value of
for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution, as we know for no solution case determinant of coefficients is equal to 0
The given equations are
2x-y-z=12
x-2y+z=-4
x+y+λz=4
Their determinant =D
For no solution case D=0
![open vertical bar table row 2 cell negative 1 end cell cell negative 1 end cell row 1 cell negative 2 end cell 1 row 1 1 lambda end table close vertical bar equals 0](data:image/png;base64,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)
=> 2(−2λ−1)+1(λ−1)−1(1+2)=0
=> −3λ−6=0
λ=−2
Hence λ=−2 for no solution.
Related Questions to study
maths-
The number of values of
for which the linear equations 4x+ky+2z=0 kx+4y+z=0 2x+2y+z=0 possess a non‐zero solution is :‐
The number of values of
for which the linear equations 4x+ky+2z=0 kx+4y+z=0 2x+2y+z=0 possess a non‐zero solution is :‐
maths-General
maths-
If
are in
then
is equal to
If
are in
then
is equal to
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are real then the value of determinant
if
If
are real then the value of determinant
if
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The system of linear equations x+y-z=6, x+2y-3z=14 and
has a unique solution if
Hence option B is the correct option
The system of linear equations x+y-z=6, x+2y-3z=14 and
has a unique solution if
Maths-General
Hence option B is the correct option
Maths-
If
then ![D equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAANCAYAAAC+ct6XAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALFJREFUeNpjYMAEP4D4PxL+AsSrgFiegYZABYgvIPGZgFgSiHOA+CEQB9HK4gAgXopDLhSIP0EdQ3VQD8QleORBwW5KC4tBcemHR34vELtgEf9PBMYLbkHjFBe4D8Si1PYtEzQocQEuIH5Ji2A2hwYlLhAPxLNxyFEU1JFAPBeP/CUg1qOFjycBcSIOuQlQTBOwDog9kPhsQOwGxNuAeBotS613SPHxB5qQQIWJJcNwAgBkUjKmYxGLegAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+RDwvbWk+PG1vPj08L21vPjwvbWF0aD44VIUcAAAAAElFTkSuQmCC)
If
then ![D equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAANCAYAAAC+ct6XAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALFJREFUeNpjYMAEP4D4PxL+AsSrgFiegYZABYgvIPGZgFgSiHOA+CEQB9HK4gAgXopDLhSIP0EdQ3VQD8QleORBwW5KC4tBcemHR34vELtgEf9PBMYLbkHjFBe4D8Si1PYtEzQocQEuIH5Ji2A2hwYlLhAPxLNxyFEU1JFAPBeP/CUg1qOFjycBcSIOuQlQTBOwDog9kPhsQOwGxNuAeBotS613SPHxB5qQQIWJJcNwAgBkUjKmYxGLegAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+RDwvbWk+PG1vPj08L21vPjwvbWF0aD44VIUcAAAAAElFTkSuQmCC)
Maths-General
maths-
Let
such that
, then maximum value of
is
Let
such that
, then maximum value of
is
maths-General
Maths-
Statement‐I : The inverse of the matrix
where
is ![B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript](data:image/png;base64,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)
Statement‐II : The inverse of singular matrix does not exist.
Hence option D is the suitable option
Statement‐I : The inverse of the matrix
where
is ![B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript](data:image/png;base64,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)
Statement‐II : The inverse of singular matrix does not exist.
Maths-General
Hence option D is the suitable option
maths-
Let
be a
matrix and let
, where
for
If the determinant of
is 2, then the determinant of the matrix
is ‐
Let
be a
matrix and let
, where
for
If the determinant of
is 2, then the determinant of the matrix
is ‐
maths-General
physics-
The power factor of the circuit is
The capacitance of the circuit is equal to
![](data:image/png;base64,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)
The power factor of the circuit is
The capacitance of the circuit is equal to
![](data:image/png;base64,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)
physics-General
physics-
In a L–R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one–fourth its initial value, is
In a L–R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one–fourth its initial value, is
physics-General
physics-
The current in the given circuit is increasing with a rate a = 4 amp/s. The charge on the capacitor at an instant when the current in the circuit is 2 amp will be :
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/610610/1/1102617/Picture43.png" alt=""
The current in the given circuit is increasing with a rate a = 4 amp/s. The charge on the capacitor at an instant when the current in the circuit is 2 amp will be :
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/610610/1/1102617/Picture43.png" alt=""
physics-General
physics-
The radius of curvature of the left and right surface of the concave lens are 10cm and 15cm respectively. The radius of curvature of the mirror is 15cm
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)
The radius of curvature of the left and right surface of the concave lens are 10cm and 15cm respectively. The radius of curvature of the mirror is 15cm
![](data:image/png;base64,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)
physics-General
physics-
An object O is kept infront of a converging lens of focal length 30cm behind which there is a plane mirror at 15cm from the lens
![](data:image/png;base64,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)
An object O is kept infront of a converging lens of focal length 30cm behind which there is a plane mirror at 15cm from the lens
![](data:image/png;base64,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)
physics-General
physics-
A diminished image of an object is to be obtained on a large screen 1 m from it. This can be achieved by
A diminished image of an object is to be obtained on a large screen 1 m from it. This can be achieved by
physics-General
physics-
A curved surface of radius R separates two medium of refractive indices
and
2 as shown in figures A and B Identify the correct statement(s) related to the formation of images of a real object O placed at x from the pole of the concave surface, as shown in figure B
![](data:image/png;base64,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)
A curved surface of radius R separates two medium of refractive indices
and
2 as shown in figures A and B Identify the correct statement(s) related to the formation of images of a real object O placed at x from the pole of the concave surface, as shown in figure B
![](data:image/png;base64,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)
physics-General