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12th Standard English Medium Maths Subject Application of Matrices and Determinants Book Back 5 Mark Questions with Solution Part - II

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. The upward speed v(t)of a rocket at time t is approximated by v(t) = at2 + bt + c, 0 ≤ t ≤ 100 where a, b and c are constants. It has been found that the speed at times t = 3, t = 6, and t = 9 seconds are respectively, 64, 133, and 208 miles per second respectively. Find the speed at time t = 15 seconds. (Use Gaussian elimination method.)

  2. Investigate for what values of λ and μ the system of linear equations x  +  2y  +  z  =  7 ,   x  +  y  +  λz   =  μ ,   x  +  3y  −  5z   =  5 has
    (i) no solution 
    (ii) a unique solution 
    (iii) an infinite number of solutions

  3. Test for consistency and if possible, solve the following systems of equations by rank method.
    2x - y + z = 2, 6x - 3y + 3z = 6, 4x - 2y + 2z = 4

  4. Find the inverse of each of the following by Gauss-Jordan method:
    \(\left[ \begin{matrix} 1 & -1 & 0 \\ 1 & 0 & -1 \\ 6 & -2 & -3 \end{matrix} \right] \)

  5. Solve the following systems of linear equations by Cramer’s rule:
    \(\frac { 3 }{ x } -\frac { 4 }{ y } -\frac { 2 }{ z } \) -1 = 0, \(\frac { 1 }{ x } +\frac { 2 }{ y } +\frac { 1 }{ z } \) - 2 = 0, \(\frac { 2 }{ x } -\frac { 5 }{ y } -\frac { 4 }{ z } \) + 1 = 0

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