Determinant

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #31

Without expanding prove that: $ \begin{vmatrix} bc & a^2 & a^2 \\ b^2 & ca & b^2 \\ c^2 & c^2 & ab \end{vmatrix} = \begin{vmatrix} bc & ab & ca \\ ab & ca & bc \\ ca & bc & ab \end{vmatrix} $
Ans: N.A.
SEE SOLUTION

Question No: #32

Without expanding, prove that: $ \begin{vmatrix} a+x & y & z \\ x & a+y & z \\ x & y & a+z \end{vmatrix} = a^2(a+x+y+z) $

Question No: #33

Without expanding, show that: $ \begin{vmatrix} a & b & c \\ x & y & z \\ p & q & r \end{vmatrix} = \begin{vmatrix} y & b & q \\ x & a & p \\ z & c & r \end{vmatrix} $

Question No: #34

Without expanding, prove that: $ \begin{vmatrix} \frac{1}{a} & 1 & bc \\ \frac{1}{b} & 1 & ca \\ \frac{1}{c} & 1 & ab \end{vmatrix} = 0 $

Question No: #35

Without expanding prove that $ \begin{vmatrix} 5 & 2 & 3 \\ 7 & 3 & 4 \\ 9 & 4 & 5 \end{vmatrix} = 0 $
Ans: N.A.
SEE SOLUTION

Question No: #36

Without expanding prove that: $ \begin{vmatrix} 1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38 \end{vmatrix} =0 $

Question No: #37

Without expanding prove that: $ \begin{vmatrix} 27 & 40 & 58 \\ 24 & 36 & 52 \\ 18 & 28 & 40 \end{vmatrix} = 0 $

Question No: #38

Without expanding, prove that: $ \begin{vmatrix} 101 & 103 & 105 \\ 104 & 105 & 106 \\ 107 & 108 & 109 \end{vmatrix} = 0 $

Question No: #39

Without expanding, prove that: $ \begin{vmatrix} 441 & 442 & 443 \\ 445 & 446 & 447 \\ 448 & 449 & 450 \end{vmatrix} = 0 $

Question No: #40

Without expanding prove that $ \begin{vmatrix} 9 & 9 & 12 \\ 1 & -3 & -4 \\ 1 & 9 & 12 \end{vmatrix} = 0 $