Matrices and Determinants · Mathematics · BITSAT

If the system of linear equation $$3 x-2 y+z=2, 4 x-3 y+3 z=-5$$ and $$7 x-5 y+\lambda z=9$$ has no solution, then $$\lambda$$ equals to

Let $$A=\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & 1 & 0 \\ 2 & 5 & 1\end{array}\right]$$ and $$49 B=\left[\begin{array}{ccc}1 & 13 & -3 \\ -4 & -3 & 12...

$$ \text { If } A=\left[\begin{array}{cc} \sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \end{array}\right] \text {, then } A(\operatorname{a...

If $$a, b, c$$ are non-zero real numbers and if the system of equations $$(a-1) x-y-z=0, -x+(b-1) y-z=0,-x-y+(c-1) z=0$$ has a non-trivial solution, t...

Given 2x $$-$$ y + 2z = 2, x $$-$$ 2y - z = $$-$$4, x + y + $$\lambda$$z = 4, then the value of $$\lambda$$ such that the given system of equation has...

Let $$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right]$$ and $$10B = \left[ {\matrix{ 4 & 2 & ...

If $$\left[ {\matrix{ 1 & { - \tan \theta } \cr {\tan \theta } & 1 \cr } } \right]{\left[ {\matrix{ 1 & {\tan \theta } \cr { - \ta...

If p $$\ne$$ a, q $$\ne$$ b, r $$\ne$$ c and the system of equations px + ay + az = 0 bx + qy + bz = 0 cx + cy + rz = 0 has a non-trivial solution, th...

If p$$\ne$$ q $$\ne$$ r and $$\left| {\matrix{ 0 & {x - p} & {x - q} \cr {x + p} & 0 & {x - r} \cr {x + q} & {x - r} & 0 \cr } } \rig...

Matrix $$A = \left| {\matrix{ x & 3 & 2 \cr 1 & y & 4 \cr 2 & 2 & z \cr } } \right|$$, if xyz = 60 and 8x + 4y + 3z = 20, then A(adj ...

An ordered pair ($$\alpha$$, $$\beta$$) for which the system of linear $$(1 + \alpha )x + \beta y + z = 2$$, $$\alpha x + (1 + \beta )y + z = 3$$, $$\...

Consider matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & 2 \cr } } \right]$$, if $${A^{ - 1}} = \alpha I + \beta A$$, where $$\alpha$$, $$\bet...