how to find addition of two matrices? Explain through examples
Question :how to find addition of two matrices? Explain through examples Solution : Addition of two matrices : Addition of two matrices are possible if and only if these matrices…
what is a matrix? Give some examples
Question : what is a matrix? Give some examples Solution : Matrix : Matrix is an arrangement of objects in rows and column. Mathematically We define a matrix as a…
how do you define an ordinary point, singular point and regular singular point of a differential equation.
Question : Define an ordinary point, singular point and regular singular point of a differential equation.singular point and regular singular point of a differential equation? Solution: Lets consider a second…
How do you find radius of convergence of the power series sum n=0 to infinity (1/2^n)*x^n
Question : How do you find radius of convergence of the power series \[\sum_{n=0}^{\infty}{\frac{1}{2^n}x^n}\] Solution : We know that radius of convergence of the power series \[\sum_{n=0}^{\infty}{a_nx^n}\] is given as\[…
how do you solve (x-2)y’+y=0 by power series solution about x=0
Question : solve (x-2)y’+y=0 by power series solution about x=0 Solution: To solve (x-2)y’+y=0 by power series (x-2)y’+y=0 about x =0 Given ode \[\left(x-2\right)y^\prime+y=0 \] (1) Let power series of…
how to Apply power series method to solve y’’-xy=x
Question : Apply power series method to solve y’’-xy=x Solution: We shall Apply power series method to solve y’’-xy=x Given ode \[y^{\prime\prime}-xy=x\] (1) Let power series \[y=\sum_{n=0}^{\infty}{a_nx^n} \] Is a…
Find the direction cosines of the sides of the triangle whose vertices are
Question : Find the direction cosines of the sides of the triangle whose vertices are (3, 5, – 4), (– 1, 1, 2) and (– 5, – 5, – 2).…
how to Show that the (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear points
Question : Show that the (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear points. Solution : To Show that the points (2, 3, 4), (–…
If a line has the direction ratios –18, 12, – 4, then what are its direction cosines
Question : If a line has the direction ratios –18, 12, – 4, then what are its direction cosines ? Solution ; If a line has the direction ratios a,…
How do you find singular value decomposition of a complex matrix?
Question : How do you find singular value decomposition of a complex matrix? Solution: Singular value decomposition: Let \[A\in M_{m\times n}\left(C\right)\] be any complex matrix. Then we define singular value…