how to subtract two matrices ? Explain
Question : how to subtract two matrices ? Explain Solution : Subtract two matrices : Subtraction of a matrix from other is defined if and only if these matrices are…
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…
function f(x)=x^3 is a one one and onto or not ?
Question : function f(x)=x^3 is a one one and onto or not ? Solution :
solved find eigen values of the matrix A=[3 0 0;0 02;0 2 0]
Question : Find eigen values of the matrix A=[3 0 0;0 02;0 2 0] Solution : Given 3 by 3 matrix \[A=\left(\begin{matrix}3&0&0\\0&0&2\\0&2&0\\\end{matrix}\right)\] It’s Eigen values are given by equation \[\left|\begin{matrix}3-\lambda&0&0\\0&-\lambda&2\\0&2&-\lambda\\\end{matrix}\right|=0\]…
solved If B is a matrix such that B^2 =B and A=I-B then which of the following is correct?
Question : If B is a matrix such that B^2 =B and A=I-B then which of the following is correct? A^2=A A^2=I AB=0 BA=0 Solution : From the Given matrix…
if f(x)=(x+2)/(x+3) and y=f^-1(x) then dy/dx is equal to
Question : If f(x)=(x+2)/(x+3) and y=f^-1(x) then dy/dx is equal to Solution : Let the Given function \[z=\frac{x+2}{x+3}\] \[xz+3z=x+2\] \[xz-x=2-3z\] x=\frac{2-3z}{z-1} This is inverse of f in terms of the…
solved find eigen values of the matrix [5 4;1 2]
Question : Find eigen values of the matrix [5 4;1 2] Solution : Given matrix \[A=\left(\begin{matrix}5&4\\1&2\\\end{matrix}\right)\] eigen values of A are given by \[\left|A-\lambda I\right|=0\] Where I is an identity…
The distinct eigen values of the matrix [1 1 0;1 1 0;0 0 0] are
Question :The distinct eigen values of the matrix [1 1 0;1 1 0;0 0 0] are (1) 0,1 (2) 1, -1 (3) 0,2 (4) 1, 2 Solution : Let the…
Solved find the sum of the series (1/n+1/(n+1)+1/(n+2)+…..+1/4n as limit n approaches infinity
Question : Find the sum of the series 1/(n+1)+1/(n+2)+…..+1/4n as limit n approaches infinity Solution : Let the sum of the series as \[L=\lim_{n\rightarrow\infty}{\left[\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\ldots..+\frac{1}{4n}\right]\ }\] \[L=\lim_{n\rightarrow\infty}{\left[\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\ldots..+\frac{1}{n+3n}\right]\ }\] \[=\lim_{n\rightarrow\infty}{\frac{1}{n}\left[\frac{n}{n}+\frac{n}{n+1}+\frac{n}{n+2}+\ldots..+\frac{n}{n+3n}\right]\ }\] \[=\lim_{n\rightarrow\infty}{\frac{1}{n}\left[\frac{1}{1+\frac{0}{n}}+\frac{1}{1+\frac{1}{n}}+\frac{1}{1+\frac{2}{n}}+\ldots..+\frac{1}{1+\frac{3n}{n}}\right]\…