Maths-
General
Easy

Question

The element in the first row and third column of the inverse of the matrix open square brackets table row 1 2 cell negative 3 end cell row 0 1 2 row 0 0 1 end table close square bracketsis

  1. – 2    
  2. 0    
  3. 1    
  4. 7    

The correct answer is: 7


    Let A equals open square brackets table row 1 2 cell negative 3 end cell row 0 1 2 row 0 0 1 end table close square brackets Þ |A| = 1
    a d j left parenthesis A right parenthesis equals open square brackets table row 1 2 cell negative 1 end cell row cell negative 2 end cell 1 1 row 7 cell negative 2 end cell 1 end table close square brackets to the power of T end exponent.
    Hence, A to the power of negative 1 end exponent equals fraction numerator a d j left parenthesis A right parenthesis over denominator vertical line A vertical line end fraction
    Þ A to the power of negative 1 end exponent equals open square brackets table row 1 cell negative 2 end cell 7 row 2 1 cell negative 2 end cell row cell negative 1 end cell 1 1 end table close square brackets . Hence, element z equals 3.

    Related Questions to study

    General
    maths-

    If A and B are non-singular square matrices of same order, then a d j left parenthesis A B right parenthesis is equal to

    If A and B are non-singular square matrices of same order, then a d j left parenthesis A B right parenthesis is equal to

    maths-General
    General
    maths-

    If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is

    If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is

    maths-General
    General
    chemistry-

    C subscript 6 H subscript 5 minus C H equals C H C H O not stretchy rightwards arrow with X on top C subscript 6 H subscript 5 C H equals C H C H subscript 2 O H  In the above sequence X can be

    C subscript 6 H subscript 5 minus C H equals C H C H O not stretchy rightwards arrow with X on top C subscript 6 H subscript 5 C H equals C H C H subscript 2 O H  In the above sequence X can be

    chemistry-General
    parallel
    General
    physics-

    A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by n left parenthesis y right parenthesis equals open square brackets k y to the power of 3 divided by 2 end exponent plus 1 close square brackets to the power of 1 divided by 2 end exponent where k equals 1.0 left parenthesis m right parenthesis to the power of negative 3 divided by 2 end exponent The refractive index of air is 1 The coordinates (x1, y(A) of the point P where the ray intersects the upper surface of the slabair boundary are

    A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by n left parenthesis y right parenthesis equals open square brackets k y to the power of 3 divided by 2 end exponent plus 1 close square brackets to the power of 1 divided by 2 end exponent where k equals 1.0 left parenthesis m right parenthesis to the power of negative 3 divided by 2 end exponent The refractive index of air is 1 The coordinates (x1, y(A) of the point P where the ray intersects the upper surface of the slabair boundary are

    physics-General
    General
    physics-

    A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by n left parenthesis y right parenthesis equals open square brackets k y to the power of 3 divided by 2 end exponent plus 1 close square brackets to the power of 1 divided by 2 end exponent where k equals 1.0 left parenthesis m right parenthesis to the power of negative 3 divided by 2 end exponent The refractive index of air is 1 Equation for the trajectory y(x) of the ray in the medium is

    A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by n left parenthesis y right parenthesis equals open square brackets k y to the power of 3 divided by 2 end exponent plus 1 close square brackets to the power of 1 divided by 2 end exponent where k equals 1.0 left parenthesis m right parenthesis to the power of negative 3 divided by 2 end exponent The refractive index of air is 1 Equation for the trajectory y(x) of the ray in the medium is

    physics-General
    General
    physics-

    A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by n left parenthesis y right parenthesis equals open square brackets k y to the power of 3 divided by 2 end exponent plus 1 close square brackets to the power of 1 divided by 2 end exponent where k equals 1.0 left parenthesis m right parenthesis to the power of negative 3 divided by 2 end exponent The refractive index of air is 1 The incident angle at B(x, y) in the medium and the slope at B are related by the formula

    A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by n left parenthesis y right parenthesis equals open square brackets k y to the power of 3 divided by 2 end exponent plus 1 close square brackets to the power of 1 divided by 2 end exponent where k equals 1.0 left parenthesis m right parenthesis to the power of negative 3 divided by 2 end exponent The refractive index of air is 1 The incident angle at B(x, y) in the medium and the slope at B are related by the formula

    physics-General
    parallel
    General
    physics-

    A point object ‘O’ is placed along x-axis An equi-convex thin lens open parentheses mu subscript g end subscript equals 1.5 close parentheses of focal length f=20cm in air is placed so that its principal axis is along x-axis Now the lens is cut at the middle (along the principal axis) and upper half is shifted along x-axis and y-axis by 20cm and 2mm respectively and right side of lower half is filled with water open parentheses mu subscript w end subscript equals fraction numerator 4 over denominator 3 end fraction close parentheses co-ordinates of image formed by lenses are

    A point object ‘O’ is placed along x-axis An equi-convex thin lens open parentheses mu subscript g end subscript equals 1.5 close parentheses of focal length f=20cm in air is placed so that its principal axis is along x-axis Now the lens is cut at the middle (along the principal axis) and upper half is shifted along x-axis and y-axis by 20cm and 2mm respectively and right side of lower half is filled with water open parentheses mu subscript w end subscript equals fraction numerator 4 over denominator 3 end fraction close parentheses co-ordinates of image formed by lenses are

    physics-General
    General
    physics-

    An object is placed 20 cm in front of a plano– convex lens of focal length 15 cm The plane surface of the lens is silvered The image will be formed at a distance

    An object is placed 20 cm in front of a plano– convex lens of focal length 15 cm The plane surface of the lens is silvered The image will be formed at a distance

    physics-General
    General
    physics-

    Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance d text  (where  end text d less than f subscript 1 end subscript comma d less than f subscript 2 end subscript text  ) end text and their centers are displaced by a vertical separation D as shown in the figure : Taking the origin of coordinates, O, at the center of the first lens, the x and y-coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by :

    Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance d text  (where  end text d less than f subscript 1 end subscript comma d less than f subscript 2 end subscript text  ) end text and their centers are displaced by a vertical separation D as shown in the figure : Taking the origin of coordinates, O, at the center of the first lens, the x and y-coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by :

    physics-General
    parallel
    General
    physics-

    For a convex lens, if real image is formed the graph between (u + v) andu or v is as follows

    For a convex lens, if real image is formed the graph between (u + v) andu or v is as follows

    physics-General
    General
    physics-

    A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 600 (see figure) If the refractive index of the material of the prism is square root of 3, which of the following is (are) correct?

    A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 600 (see figure) If the refractive index of the material of the prism is square root of 3, which of the following is (are) correct?

    physics-General
    General
    biology

    Man and mouse cells are treated with red rhodamine and Green fluorescent dyes separately and then are made to fuse. The resultant cells when kept at 37ºC, the distribution of dye on the surface of cell will be like–

    Man and mouse cells are treated with red rhodamine and Green fluorescent dyes separately and then are made to fuse. The resultant cells when kept at 37ºC, the distribution of dye on the surface of cell will be like–

    biologyGeneral
    parallel
    General
    chemistry-

    Which of the following statements is not correct?

    Which of the following statements is not correct?

    chemistry-General
    General
    maths-

    A d j. left parenthesis A B right parenthesis minus left parenthesis A d j. B right parenthesis left parenthesis A d j. A right parenthesis equals