Determinant

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

Click on each question to see answer & solution.

Question No: #131

Show that the equations `(\lambda+a)x+\lambda\y+\lambda\z=0`, `\lambda\x+(\lambda+b)y+\lambda\z=0` and `\lambda\x+\lambda\y+(\lambda+c)z=0` have non-zero solutions if `\frac{1}{\lambda}=-(1/a+1/b+1/c)`

Question No: #132

Solve by Cramer's rule: `3x+y+z=2`, `2x-4y+3z=-1`, `4x+y-3z=-11`

Question No: #133

Solve by Cramer's rule: `x-2y+z=-1`, `3x+y-2z=4`, `y-z=1`

Question No: #134

Solve by Cramer's rule: `2x-y+z=6`, `x+2y+3z=3`, `3x+y-z=4`

Question No: #135

Solve by Cramer's rule: `x+y+z=1`, `ax+by+cz=k`, `a^2x+b^2y+c^2z=k^2` where [`a\neb\nec`]

Question No: #136

Solve by Cramer's rule: `1/x+1/y+1/z=1`, `2/x+5/y+3/z=0`, `1/x+2/y+4/z=0`

Question No: #137

Solve by Cramer's rule: `1/x+2/y+1/z=1/2`, `4/x+2/y-3/z=2/3`, `3/x-4/y+4/z=1/3`

Question No: #138

If the points `(a_1, b_1)`, `(a_2, b_2)` and `(a_1+a_2, b_1+b_2)` are collinear, then show that `a_1b_2 = a_2b_1`

Question No: #139

If the coordinates of vertices of a triangle are `[m(m+1), m+1]`, `[(m+1)(m+2), m+2]` and `[(m+2)(m+3), m+3]`, then prove that the area of said triangle is not depend on `m`.