Embibe Experts Solutions for Chapter: Applications of Matrices and Determinants, Exercise 1: Tamilnadu Board-2018

If $A$ is a scalar matrix with scalar $k\ne 0$, of order $3$ then $A^{-1}$ is 

Find the adjoint of the matrix $A=\left[\begin{array}{rr}1& 2\\ 3& -5\end{array}\right]$ and verify the result $A\left(\mathrm{adj}A\right)=\left(\mathrm{adj}A\right)A=\left|A\right|·I$.

Solve the following non-homogeneous equations by using the determinant method.

$2x+2y+z=5$

$x-y+z=1$

$3x+y+2z=4$

Discuss the solutions of the following system of equations for all values of $\lambda$.

$x+y+z=2,2x+y-2z=2,\lambda x+y+4z=2$.

In the homogeneous system $\rho \left(A\right)$ is less than the number of unknowns, then the system has :

If $A$ is a scalar matrix with scalar $k\ne 0$, of order $3$, then $A^{-1}$ is :

For what values of $\mu$ the system of homogeneous equations $x+y+3z=0; 4x+3y+\mu z=0; 2x+y+2z=0$ have : only trivial solution.

For what values of $\mu$ the system of homogeneous equations $x+y+3z=0; 4x+3y+\mu z=0; 2x+y+2z=0$ have : infinitely many solutions.