Recent questions tagged rank-of-matrix

A $2 n \times 2 n$ matrix $A=\left[a_{i j}\right]$ has its elements as$$ a_{i j}=\begin{cases} \beta & \text { if }(i+j) \text { is odd } \\ -\beta & \text { if }(i+j) \t...

A matrix $M$ is constructed by stacking three column vectors $v_{1}, v_{2}, v_{3}$ as$$ M=\left[\begin{array}{lll} v_{1} & v_{2} & v_{3} \end{array}\right]$$Choose the se...

The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha}{\beta}$ is __________ (rounded off to the nearest integer).$$A=\left[\begin{array}{cc}1 & 4 \\-3 &...