# Tagged Questions

Question about determinants, computation or theory. If $E$ is a vector space of dimension $d$, then we can compute the determinant of a $d$-uple $(v_1,\ldots,v_d)$ with respect to a basis.

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### Finding out of a set of 3x1 matrices are linearly independent or dependent

I know how to determine if any $2 \times 2$ matrix or $3 \times 3$ matrix is linearly dependent/independent; It's easy, as long as the determinant of the matrix $\ne 0 \implies$ linearly independent, ...
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### Determinant of a block rectangular matrix

Assume that $a \in \mathbb{R}^{n \times 1}, b \in \mathbb{R}, P \in \mathbb{R}^{n \times n}, u \in \mathbb{R}^{n \times 1}, x \in \mathbb{R}^{n \times 1}$ and $\lambda \in \mathbb{R}$. Now I want to ...
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### Proving Determinants equal to some expressions(tips and tricks) [on hold]

Is there any trick or a step by step method that I can use to prove a certain determinant equal to a complicated expression by solving it? Also when I try to open the determinant to prove it equal to ...
If a matrix $A= \begin{bmatrix}2a & 2b \\ 2c & 0 \\ \end{bmatrix}$ and matrix $B=2 \begin{bmatrix}a & b \\ c & 0 \\ \end{bmatrix}$, then how is $A=2B$ also explain how is this ...