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Calculate the correlation coefficient from the following data:
engineering mathematics updated 9.4 years ago by teamques10 ★ 70k
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Show that $$A= \begin{bmatrix} 7 & 4 & 4 \\ -1 & 4 & 7 \\ -1 & -4 & -4 \\ \end{bmatrix}$$ is derogatory.
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Show that the matrix A is diagonalizable, find its diagonal form and transforming matrix, if $$A= \begin{bmatrix} -9 & 4 & 4 \\ -8 & 3 & 4 \\ -16 & 8 & 7 \\ \end{bmatrix}$$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Show that the matrix $$ A= \begin{bmatrix} 5 & -6 & -6 \\ -1 & 4 & 2 \\ 3 & -6 & -4 \\ \end{bmatrix}$$ is derogatory.
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Find the eigen values of $A^3 + 5A + 8I$ from given matrix.
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Determine whether matrix A is derogatory $$A= \begin{bmatrix} 2 & 1 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & 2 \\ \end{bmatrix} $$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Evaluate using Cauchy's Residue theorem $\phi_c\dfrac {1-2z}{(z-2)(z-2)}dz$ where c is $|z| = 1.5. $
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Expand $f(z)=\dfrac z{(z-2)(z-1)}$ in the regions i) $|z| < 1$ ii) $1< |z|$, iii) $|z| > 2. $
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Evaluate the line integral along the path $y = x. $
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Evaluate $\int\limits_0^{\infty}\dfrac {dx}{(x^2+a^2)^3}, a > 0$ using contour integration
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Find all possible Laurent's expansion of the function $F(z)=\dfrac {7z-2}{z(z-2)(z+1)}$ about $z=-1$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Evaluate $\int\dfrac {z+2}{z^3-2z^2}dz$ where C is the circle $|z - 2- i|= 2$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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show that $\int \log z\space dz=2\pi i$ where C is the unit circle in the z-plane
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Evaluate the followin g integral by contour integration. $\int\limits_{\infty}^{\infty}\dfrac {x^2dx}{(x^2+1)(x^2+4)}$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Find Laurent's series which represents the functions the function $f(z)= \dfrac 2{(z-1)(z-2)}$ when (i) $|z|< 1$ (ii) $1< |z|<2$ (iii) $|z|> 2.$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Evaluate $\int\dfrac {z+3}{z^2+2z+5}dz$ where C is the circle (i) $|z| = 1$. (ii) $|z+1-i|= 2.$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Using cauchy's residue theorem, show that $\int\limits_0^{2\pi}\dfrac {\cos 2\theta}{5+4\cos \theta}d\theta =\dfrac \pi6$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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Obtain all Taylor's and Laurent's series expansions of functions $\dfrac {(z-2)(z+2)}{(z+1)(z+4)}$ about $z = 0$
engineering mathematics updated 9.5 years ago by teamques10 ★ 70k
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