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    Mid Suggestion For NAME and ME

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    Shakil Mahmud

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    Mid Suggestion For NAME and ME

    Uploaded by

    Shakil Mahmud
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    Mid Suggestion for NAME and ME

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    13 views2 pages

    Mid Suggestion For NAME and ME

    Uploaded by

    Shakil Mahmud

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    Matrix

    Q-1.(a) Define the following with example:


    (i) Non-singular matrix
    (ii) Unit matrix
    (iii) Null matrix (iv) Scalar matrix
    (b) Define orthogonal matrix. Prove that the following matrix is orthogonal:
    cos 0 sin  
     0 1 0 

     sin  0 cos 

     3 − 3 4
    (c). If A= 2 − 3 4 , then find A −1 .
    0 − 1 1

    (d). Test for consistency, the given system of equations and solve if it is
    consistent,
    x + 2y + 3z = 1, 2x + 3y + 2z = 2, 3x + 3y + 4z = 1.
    𝟏 𝟑 𝟏 −𝟐 −𝟑
    (e) Find the rank of the Matrix [ 𝟏 𝟒 𝟑 −𝟏 −𝟒 ]
    𝟐 𝟑 −𝟒 −𝟕 −𝟑
    𝟑 𝟖 𝟏 −𝟕 −𝟖
    (f) solve the system by inverse matrix method
    𝟐𝒙 + 𝟑𝒚 − 𝟓𝒛 = 𝟕
    𝒙 − 𝟒𝒚 + 𝒛 = 𝟒
    𝟑𝒙 𝟏 𝟐𝒛
    − 𝒚− =𝟏
    𝟓 𝟓 𝟓
    Q-2(a). Derive partial differential equation by elimination of arbitrary function
    ∅ from the equation ∅(𝒖, 𝒗) = 𝟎 where 𝒖 𝒂𝒏𝒅 𝒗 are functions of 𝒙, 𝒚 𝒂𝒏𝒅 𝒛 P-
    1.11, Rule-2, Art-1.11 Mist-2019
    (b) Define partial differential equation. Show that the differential equation of
    all cones which have their vertex at the origin is 𝒑𝒙 + 𝒒𝒚 = 𝒛 verify that 𝒚𝒛 +
    𝒛𝒙 + 𝒙𝒚 = 𝟎 is a surface satisfying the above equation
    (c). Form partial differential equation eliminating arbitrary function ∅ from
    the equation ∅(𝒙𝟐 + 𝒚𝟐 + 𝒛𝟐 , 𝒛𝟐 − 𝟐𝒙𝒚) = 𝟎.
    (d). Discuss about the working rules of Lagrange’s method. Applying
    Lagrange’s method solve (𝒙 + 𝟐𝒛)𝒑 + (𝟒𝒙𝒛 − 𝒚)𝒒 = 𝟐𝒙𝟐 + 𝒚
    (e) Applying Lagrange’s method solve
    (ii) {(𝒃 − 𝒄)/𝒂}𝒚𝒛𝒑 + {(𝒄 − 𝒂)/𝒃}𝒛𝒙𝒒 = {(𝒂 − 𝒃)/𝒄}𝒙𝒚 P-2.8 , S 2.10 ,Art-2.9
    Mist Exam -2018, Mist Exam -2019
    (f).Promote the equation of integral surface satisfying the equation,
    𝟒𝒚𝒛𝒑 + 𝒒 + 𝟐𝒚 = 𝟎 𝒂𝒏𝒅 𝒑𝒂𝒔𝒔𝒊𝒏𝒈 through 𝒚𝟐 + 𝒛𝟐 = 𝟏 , 𝒙 + 𝒛 = 𝟐
    P-2.29 ex 5 . mist-2019

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