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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 6.0 years ago by teamques10 ★ 70k
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State Cayley - Hamilton Theorem, hence deduce that $A^8 = 6251$ where $A = \begin{bmatrix} 1 & 2 \\ 2 & -1 \end{bmatrix}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Prove that eigen values of Hermitian matrix are real
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Express P(x) = $7+8x+9x^2$ as a linear combination of $P_1(x)=2+x+4x^2,P_2(x)=1-x+3x^2,P_3(x)=2+x+5x^2$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find a vector orthogonal to both of u=(-6,4,2) , v=(3,1,5)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Let $R^3$ have the euclidian linear product use grame-schmidt process to transform the bias basis ${u_1,u_2,u_3}$in to an orthogonal basis where $u_1=(1,,1,1),u_2=(-1,1,0),u_3=(1,2,1)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Let V= $R^3$ show that W is a subspace of $R^3$ where W={(a,b,c)=a+b+c=0},that is W consist of all vectors where the sum of their component is zero.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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State Cauchy- Shwartz Inequality in $R^3$ and verify it for u =(-4,2,1) and v = (8,-4,-2)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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State and prove Cauchy - Schwartz inequality verify the inequality for vectors V = (-4,2,1) and V = (8,-4,-2)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find an orthogonal basis for the subspaces of $R^3$ by applying Gram-Schmidt process where S = {(1,2,0), (0,3,1)}
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Construct an orthonormal basis or $R^2$ by applying Gram Schmidt orthogonalization to S = {[3,1], [2,2]}
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find an orthonormal basis of the following subspace of $R^3$, S = {[1, 2, 0][0, 3, 1]}
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find a vector orthogonal to both u = (-6, 4, 2) & v = (3, 1, 5)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Verify Cauchy - Schwartz Inequality for the vectors u = (-4,2,1) & v = (8, -4, 2)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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State Cauchy - Schwartz inequality and hence show that $(x^2 + y^2 + z^2)^{\frac{1}{2}} \geq \frac{1}{13} (3x + 4y + 12z)$, x,y,z are positive.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using Rayleigh- ritz method solve the boundry value problem $J=\int_0^1 (xy +\frac {1}{2}y'^2)dx ; 0\le X\le 1$ given y(0)=0,y(1)=0 where $\bar y(x)=c_0+c_1x+c_2 x^2$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the extremals of the function $\int_0^{\pi/2} (y'^2-y^2+2xy)dy y(0)=0 , y(\pi /2)=0$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using Rayleigh- ritz method solve the boundry value problem using two degree polynomial as initial solution..$J=\int_0^1 (2xy +y^2-y'^2)dx ; 0\le X\le 1$ given y(0)=0,y(1)=0
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the extremals of $\int_{x_0}^{x_1}(2xy+y^{''2})$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the extremal of $\int_{0}^{1} {(x y+y^2-2y^2 y')dx}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using Rayleigh - Ritz method, find an appropriate solution for the extremal of the functional $I[y(x)] = \int\limits_{0}^{1} xy + \frac{1}{2}(y')^2 dx$ subject to y(0) = y(1) = 0.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Solve the boundary value problem $$I = \int\limits_{0}^{1} 2xy - y^2 - (y')^2 dx$$ Given y(0) = y(1) = 0 by Rayleigh - Ritz method.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the plane curve of fixed perimeter and maximum area
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Determine the function that gives the shortest distance between two points
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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980
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Find the curve y = f(x) for which $ \int_{x_1}^{x_2} y \sqrt{1+(y')^2} \, dx $ is minimum subject to the constraint $ \int_{x_1}^{x_2} \sqrt{1+(y')^2} \, dx $ = l
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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