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Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -8, and 2 + 5i
4, -8, and 2 + 5i
Q. Write down the applications of Differential equations.
Q. Explain the Mathematical modeling of 2nd and higher order ordinary differential equation.
Q. Explain the Mathematical modeling of first order differential equation.
Q. Show that the transformation between the coordinates X1, X2, X3 and X1’ , X2’ , X3’ defined by
X1’=1/3(2x1+2x2-x3)
X2’=1/3(2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
Is orthogonal and left-handed(improper)
X1’=1/3(2x1+2x2-x3)
X2’=1/3(2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
Is orthogonal and left-handed(improper)
Q. A second order tensor has components ■(2&1&0@1&-3&-1@0&-1&2) in OX1X2X3. The transformation between the coordinates X1, X2, X3 and X1’ , X2’ , X3’ is defined by
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
(i)Find its components in the new system OX1’X2’X3’.(By using Matrix Formula).
(ii) Compute A’32 in the new system.(By using component formula)
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
(i)Find its components in the new system OX1’X2’X3’.(By using Matrix Formula).
(ii) Compute A’32 in the new system.(By using component formula)
Q. Write transformation equations for a second order tensor Aij w.r.t this transformation and verify A’ii=Aii
Q. A vector A in OX1X2X3 has components (2, 1, -2). Find its components in OX1’X2’X3’. The transformation between the coordinates X1, X2, X3 and X1’ , X2’ , X3’ is defined by
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
Q. Show that the transformation between the coordinates X1, X2, X3 and X1’ , X2’ , X3’ defined by
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
Is orthogonal and left-handed(improper)
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
Is orthogonal and left-handed(improper)
If H is a subgroup of G of index 2, prove that H is normal in G.
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#339914 on Dec 2023
#339914 on Dec 2023