Maths-
General
Easy

Question

If A equals open square brackets table row alpha 0 row 1 1 end table close square brackets and B equals open square brackets table row 1 0 row 3 1 end table close square brackets comma then value of alpha for which A to the power of 2 end exponent equals B is

  1. 1    
  2. -1    
  3. i    
  4. no real value of alpha    

hintHint:

We are given two matrices A and B. One of the element of matrix A is missing. It is denoted by a variable α. We are given the condition that the matrices satisfy. We have to use the conditon to find the value of the variable.

The correct answer is: no real value of alpha


    The given matrices are as follows:
    A space equals open square brackets table row alpha 0 row 1 1 end table close square brackets
    B space equals open square brackets table row 1 0 row 3 1 end table close square brackets
    The given condition is A= B
    We will first find the value of A2. We will multiply the matrix A by itself. The we will substitute the value in the condition.  We will get two matrices on both side of equal sign. We will compare the elements of the matrices.
    We will find A
    A squared equals open square brackets table row alpha 0 row 1 1 end table close square brackets times open square brackets table row alpha 0 row 1 1 end table close square brackets
space space space space equals open square brackets table row cell alpha squared plus 0 end cell cell 0 space plus 0 end cell row cell alpha space plus 1 end cell cell 0 plus space 1 end cell end table close square brackets
space space space space equals open square brackets table row cell alpha squared end cell 0 row cell alpha space plus 1 end cell 1 end table close square brackets
space space space space space
    Now we will substitute this value in the condition.
    open square brackets table row cell alpha squared end cell 0 row cell alpha space plus space 1 end cell 1 end table close square brackets equals open square brackets table row 1 0 row 3 1 end table close square brackets
     
    We will compare the elements now.
    α2 = 1
    α + 1 = 3
    If we see α cannot satisfy both the conditions simultaneously.
    So, It doesn't have any real value.
    The right option is " no real value of α".

    For such questions, we should know how to multiply to matrices. When there is equal sign between two matrices, the elements of both the matrix should be equal.

    Related Questions to study

    General
    Maths-

    For the primitive integral equation y d x plus y to the power of 2 end exponent d y equals x d y comma x element of R comma y greater than 0 comma y equals y open parentheses x close parentheses comma y open parentheses 1 close parentheses equals 1 comma then y open parentheses negative 3 close parentheses is

    For such questions, we should know different method of differentiation and integration.

    For the primitive integral equation y d x plus y to the power of 2 end exponent d y equals x d y comma x element of R comma y greater than 0 comma y equals y open parentheses x close parentheses comma y open parentheses 1 close parentheses equals 1 comma then y open parentheses negative 3 close parentheses is

    Maths-General

    For such questions, we should know different method of differentiation and integration.

    General
    Maths-

    The differential equation of all circles which pass through the origin and whose centre lies on y-axis is

    For such questions, we should know the equation of cricle with its centre at a point other than origin.

    The differential equation of all circles which pass through the origin and whose centre lies on y-axis is

    Maths-General

    For such questions, we should know the equation of cricle with its centre at a point other than origin.

    General
    Maths-

    The differential equation of all parabolas whose axis are parallel to y-axis is

    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.

    The differential equation of all parabolas whose axis are parallel to y-axis is

    Maths-General

    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.

    parallel
    General
    Maths-

    Solution of the differential equation open parentheses fraction numerator d y over denominator d x end fraction close parentheses to the power of 2 end exponent minus fraction numerator d y over denominator d x end fraction open parentheses e to the power of x end exponent plus e to the power of negative x end exponent close parentheses plus 1 equals 0 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 open parentheses fraction numerator d y over denominator d x end fraction close parentheses to the power of 2 end exponent minus fraction numerator d y over denominator d x end fraction open parentheses e to the power of x end exponent plus e to the power of negative x end exponent close parentheses plus 1 equals 0 is given by

    Maths-General

    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.

    General
    Maths-

    The differential equation of all ellipse centred at the origin and major and minor axes along coordinate axes is

    The differential equation of all ellipse centred at the origin and major and minor axes along coordinate axes is

    Maths-General
    General
    Maths-

    Area of the region bounded by y equals tan invisible function application x comma tangent drawn to the curve at x equals fraction numerator pi over denominator 4 end fraction and the x minusaxis is

    Area of the region bounded by y equals tan invisible function application x comma tangent drawn to the curve at x equals fraction numerator pi over denominator 4 end fraction and the x minusaxis is

    Maths-General
    parallel
    General
    Maths-

    Maximum value of x left parenthesis 1 minus x right parenthesis to the power of 2 end exponent, when 0 less or equal than x less or equal than 2, is

    Maximum value of x left parenthesis 1 minus x right parenthesis to the power of 2 end exponent, when 0 less or equal than x less or equal than 2, is

    Maths-General
    General
    Maths-

    If x = c o s to the power of negative 1 end exponentt, y = square root of 1 minus t to the power of 2 end exponent end root , then y subscript 2 end subscript equals

    If x = c o s to the power of negative 1 end exponentt, y = square root of 1 minus t to the power of 2 end exponent end root , then y subscript 2 end subscript equals

    Maths-General
    General
    Physics-

    Two capacitors C subscript 1 end subscript equals 2 mu F and C subscript 2 end subscript equals 6 mu F in series, are connected in parallel to a third capacitor C subscript 3 end subscript equals 4 mu F. This arrangement is then connected to a battery of e.m.f. = 2V, as shown in the figure. How much energy is lost by the battery in charging the capacitors

    Two capacitors C subscript 1 end subscript equals 2 mu F and C subscript 2 end subscript equals 6 mu F in series, are connected in parallel to a third capacitor C subscript 3 end subscript equals 4 mu F. This arrangement is then connected to a battery of e.m.f. = 2V, as shown in the figure. How much energy is lost by the battery in charging the capacitors

    Physics-General
    parallel
    General
    Physics-

    The combination of capacitors with C subscript 1 end subscript equals 3 mu F comma C subscript 2 end subscript equals 4 mu F and C subscript 3 end subscript equals 2 mu F is charged by connecting AB to a battery. Consider the following statements
    I. Energy stored in C subscript 1 end subscript= Energy stored in C subscript 2 end subscript + Energy stored in C subscript 3 end subscript
    II. Charge on C1 = Charge on C2 + Charge on C3
    III. Potential drop across C1 = Potential drop across C2 = Potential drop across C3
    Which of these is/are correct

    The combination of capacitors with C subscript 1 end subscript equals 3 mu F comma C subscript 2 end subscript equals 4 mu F and C subscript 3 end subscript equals 2 mu F is charged by connecting AB to a battery. Consider the following statements
    I. Energy stored in C subscript 1 end subscript= Energy stored in C subscript 2 end subscript + Energy stored in C subscript 3 end subscript
    II. Charge on C1 = Charge on C2 + Charge on C3
    III. Potential drop across C1 = Potential drop across C2 = Potential drop across C3
    Which of these is/are correct

    Physics-General
    General
    Physics-

    Consider a parallel plate capacitor of 10 mu rightwards arrow over short leftwards arrow F (micro-farad) with air filled in the gap between the plates. Now one half of the space between the plates is filled with a dielectric of dielectric constant 4, as shown in the figure. The capacity of the capacitor changes to

    Consider a parallel plate capacitor of 10 mu rightwards arrow over short leftwards arrow F (micro-farad) with air filled in the gap between the plates. Now one half of the space between the plates is filled with a dielectric of dielectric constant 4, as shown in the figure. The capacity of the capacitor changes to

    Physics-General
    General
    Physics-

    In the figure a capacitor is filled with dielectrics. The resultant capacitance is

    In the figure a capacitor is filled with dielectrics. The resultant capacitance is

    Physics-General
    parallel
    General
    Physics-

    Equivalent capacitance between A and B is

    Equivalent capacitance between A and B is

    Physics-General
    General
    Physics-

    In the figure, three capacitors each of capacitance 6p F are connected in series. The total capacitance of the combination will be

    In the figure, three capacitors each of capacitance 6p F are connected in series. The total capacitance of the combination will be

    Physics-General
    General
    Physics-

    Two capacitors A and B are connected in series with a battery as shown in the figure. When the switch S is closed and the two capacitors get charged fully, then

    Two capacitors A and B are connected in series with a battery as shown in the figure. When the switch S is closed and the two capacitors get charged fully, then

    Physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.