Question
If
then
exists
- For all real
- For positive real
only
- For negative real
only
- None of these
Hint:
We are given a matrix. We have to find the condition on the variable x so that the inverse of the matrix exist.
The correct answer is: For all real 
The given matrix is

The inverse of matrix exists if it's determinant is non zero.
We will find the determinant of the given matrix.

The determinant of the given matrix is non zero. It is also constant. It does not depend on the value of x.
So, the A-1 exist for all real x.
Whenever we have to find the inverse of the matrix, we should check the determinant of the matrix. The determinant must be non zero for a inverse to exist.
Related Questions to study
If
etc., and
etc. and
then
If
etc., and
etc. and
then
If
and
then value of
for which
is
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and
then value of
for which
is
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then
is
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then
is
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For such questions, we should know the equation of cricle with its centre at a point other than origin.
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For such questions, we should know the equation of cricle with its centre at a point other than origin.
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For such questions, we should know how to write the equation of a parabola. The axis of parabola can be parallel to x or y axis. So, we have to write the equation accordingly.
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For such questions, we should know how to write the equation of a parabola. The axis of parabola can be parallel to x or y axis. So, we have to write the equation accordingly.
Solution of the differential equation
is given by
When we get multipliction of two brackets equal to zero, any of the bracket can be zero or both of the brackets can be zero. It is decided based on the conditions in the equation.
Solution of the differential equation
is given by
When we get multipliction of two brackets equal to zero, any of the bracket can be zero or both of the brackets can be zero. It is decided based on the conditions in the equation.