Proof | Property of Determinant (7)
Suppose that a matrix A is matrix. Then if a matrix is multiplied by k, the determinant is multiplied by $$\le […]
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Suppose that a matrix A is matrix. Then if a matrix is multiplied by k, the determinant is multiplied by $$\le […]
もっと読む →If two rows of a matrix are equal, its determinant is zero : $$\left|\begin{array}{ccc}a_{11}& a_{12} […]
もっと読む →If two rows of a matrix are interchanged, the sign of its determinant is changed : $$\left|\begin{array}{ccc}a […]
もっと読む →If a multiple of one row of a matrix is added to another row, its determinant is equal to original determinant […]
もっと読む →Proof We prove when . If we compute the determinant of RHS by expansion across the 2nd row, we have \begin{eqn […]
もっと読む →Proof We prove when . If we compute the determinant of LHS by expansion across the 2nd row, we have \begin{eqn […]
もっと読む →A symmetric matrix is a matrix A such that $$A^{t}=A $$ where is a transposed matrix of A. Such a matrix is ne […]
もっと読む →Proof Suppose that A is an matrix as follows: $$A=\begin{bmatrix}a_{11} &a_{12}&\cdots&a_{1m}\\a_{ […]
もっと読む →Proof \begin{eqnarray*}M_{X+Y}(t)&=&E[\mathrm{e}^{(X+Y)t}]\\&=&E[\mathrm{e}^{Xt}\mathrm{e}^{Yt […]
もっと読む →Proof \begin{eqnarray*}M_{aX+b}(t)&=&E[\mathrm{e}^{(aX+b)t}]\\&=&E[\mathrm{e}^{atX}\mathrm{e}^ […]
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