Maths-
General
Easy

Question

Which of the following is not true

  1. Every skew-symmetric matrix of odd order is non-singular    
  2. If determinant of a square matrix is non-zero, then it is non singular    
  3. Adjoint of symmetric matrix is symmetric    
  4. Ad joint of a diagonal matrix is diagonal    

The correct answer is: Every skew-symmetric matrix of odd order is non-singular


    Every skew symmetric matrix of odd order is singular. So option (a) is incorrect.

    Related Questions to study

    General
    maths-

    Which one of the following statements is true

    Which one of the following statements is true

    maths-General
    General
    maths-

    The inverse of open square brackets table row 1 2 3 row 0 1 2 row 0 0 1 end table close square bracketsis

    The inverse of open square brackets table row 1 2 3 row 0 1 2 row 0 0 1 end table close square bracketsis

    maths-General
    General
    Maths-

    The inverse of matrix A equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square bracketsis

    A real number multiplicative inverse is the number that, when multiplied by the original number, produces 1 (the identity). Because a× 1/a= 1 is the multiplicative inverse of a. When the inverse of a matrix is multiplied by a given matrix, it produces a multiplicative identity. For example, the inverse of a matrix A is A-1 and A.A-1=A-1.A=I, where I is the identity matrix.
    A square matrix with one on the diagonal and zeros everywhere else is known as an identity matrix. Think of the identity matrix as the matrix's prime number.
    An invertible matrix is one for which it is possible to calculate the inverse matrix and for which the determinant is not zero.

    The inverse of matrix A equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square bracketsis

    Maths-General

    A real number multiplicative inverse is the number that, when multiplied by the original number, produces 1 (the identity). Because a× 1/a= 1 is the multiplicative inverse of a. When the inverse of a matrix is multiplied by a given matrix, it produces a multiplicative identity. For example, the inverse of a matrix A is A-1 and A.A-1=A-1.A=I, where I is the identity matrix.
    A square matrix with one on the diagonal and zeros everywhere else is known as an identity matrix. Think of the identity matrix as the matrix's prime number.
    An invertible matrix is one for which it is possible to calculate the inverse matrix and for which the determinant is not zero.

    parallel
    General
    chemistry-

     A space a n d space B respectively are

     A space a n d space B respectively are

    chemistry-General
    General
    physics-

    Light is incident normally in face AB of a prism as shown in figure A liquid of refractive index m is placed on face AC of the prism The prism is made of glass of refractive index 3/2 The limits of m for which total internal reflection takes place on face AC is

    Light is incident normally in face AB of a prism as shown in figure A liquid of refractive index m is placed on face AC of the prism The prism is made of glass of refractive index 3/2 The limits of m for which total internal reflection takes place on face AC is

    physics-General
    General
    physics-

    An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod Then the refractive index of the liquid is

    An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod Then the refractive index of the liquid is

    physics-General
    parallel
    General
    physics-

    A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index n subscript 2 end subscript open parentheses n subscript 1 end subscript greater than n subscript 2 end subscript close parentheses A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD, is given by

    A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index n subscript 2 end subscript open parentheses n subscript 1 end subscript greater than n subscript 2 end subscript close parentheses A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD, is given by

    physics-General
    General
    physics-

    A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q The reflected (R) and transmitted (T) intensitites, both as function of q , are plotted The correct sketch is

    A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q The reflected (R) and transmitted (T) intensitites, both as function of q , are plotted The correct sketch is

    physics-General
    General
    physics-

    A point source S is placed at the bottom of different layers as shown in the figure The refractive index of bottom most layer is m0 The refractive index of any other upper layer is mu subscript left parenthesis n right parenthesis end subscript equals mu subscript 0 end subscript minus fraction numerator mu subscript 0 end subscript over denominator 4 n minus 18 end fraction text  where  end text n equals 1 comma 2 comma horizontal ellipsis horizontal ellipsis A ray of light with angle i slightly more than 30° starts from the source S Total internal reflection takes place at the upper surface of a layer having n equal to

    A point source S is placed at the bottom of different layers as shown in the figure The refractive index of bottom most layer is m0 The refractive index of any other upper layer is mu subscript left parenthesis n right parenthesis end subscript equals mu subscript 0 end subscript minus fraction numerator mu subscript 0 end subscript over denominator 4 n minus 18 end fraction text  where  end text n equals 1 comma 2 comma horizontal ellipsis horizontal ellipsis A ray of light with angle i slightly more than 30° starts from the source S Total internal reflection takes place at the upper surface of a layer having n equal to

    physics-General
    parallel
    General
    physics-

    An insect starts moving up in a liquid from point O of variable refractive index mu equals mu subscript 0 end subscript left parenthesis 1 plus a y right parenthesis where y is depth of liquid from the surface If u is the speed of insect, its apparent speed to the observer E immediatly after insect start moving

    An insect starts moving up in a liquid from point O of variable refractive index mu equals mu subscript 0 end subscript left parenthesis 1 plus a y right parenthesis where y is depth of liquid from the surface If u is the speed of insect, its apparent speed to the observer E immediatly after insect start moving

    physics-General
    General
    maths-

    If A equals open square brackets table row 1 cell negative 2 end cell row 5 3 end table close square brackets, then A plus A to the power of T end exponentequals

    If A equals open square brackets table row 1 cell negative 2 end cell row 5 3 end table close square brackets, then A plus A to the power of T end exponentequals

    maths-General
    General
    maths-

    The inverse of the matrix open square brackets table row 3 cell negative 2 end cell row 1 4 end table close square bracketsis

    The inverse of the matrix open square brackets table row 3 cell negative 2 end cell row 1 4 end table close square bracketsis

    maths-General
    parallel
    General
    maths-

    The ad joint of open square brackets table row 1 1 1 row 1 2 cell negative 3 end cell row 2 cell negative 1 end cell 3 end table close square bracketsis

    The ad joint of open square brackets table row 1 1 1 row 1 2 cell negative 3 end cell row 2 cell negative 1 end cell 3 end table close square bracketsis

    maths-General
    General
    chemistry-

    The reaction of ethanol with H subscript 2 S O subscript 4 does not give:

    The reaction of ethanol with H subscript 2 S O subscript 4 does not give:

    chemistry-General
    General
    chemistry-

    An aqueous solution of ethyl alcohol:

    An aqueous solution of ethyl alcohol:

    chemistry-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.