Define Matrix Rank and explain how to find the rank of a matrix using echelon form.
Determine the rank of a matrix using normal form.
Explain the Gauss-Jordan Method to find the inverse of a non-singular matrix.
Find the inverse of a non-singular matrix using the Gauss-Jordan method.
Solve a system of Homogeneous Linear Equations.
Solve a system of Non-Homogeneous Linear Equations.
Discuss the consistency of a system of linear equations using matrix rank.
State and explain the conditions for the existence of unique, infinite, and no solutions to a system of linear equations.
Explain the Gauss-Seidel Iteration Method for solving simultaneous equations.
Solve a system of linear equations using the Gauss-Seidel iteration method.
unit-2 
Define Linear Transformation and Orthogonal Transformation.
Define Eigenvalue and Eigenvector and explain their properties.
Find the eigenvalues and eigenvectors of a given matrix.
Explain the process of Matrix Diagonalization.
State and apply the Cayley-Hamilton Theorem.
Find the inverse of a matrix using the Cayley-Hamilton theorem.
Find higher powers of a matrix using the Cayley-Hamilton theorem.
Define a Quadratic Form and determine its nature (positive definite, negative definite, indefinite).
Reduce a quadratic form to canonical form using orthogonal transformation.
Explain the significance and applications of eigenvalues, eigenvectors, and quadratic forms in engineering and data analysis.
UNIT-3
Define Limit of a Function and Continuity of a Function and explain their properties.
State and explain Rolle's Theorem with geometrical interpretation.
State and explain Lagrange's Mean Value Theorem with geometrical interpretation and applications.
State and explain Cauchy's Mean Value Theorem.
Verify Rolle’s theorem for a given function.
Verify Lagrange’s Mean Value Theorem for a given function and find the corresponding value of c.
Apply Cauchy’s Mean Value Theorem to suitable functions.
Expand a function using Taylor Series.
Explain the steps involved in tracing curves in Cartesian coordinates.
Trace curves in Cartesian coordinates by identifying symmetry, intercepts, tangents, and asymptotes.
Related important questions
UNIT-4
Define limits and continuity for functions of several variables and explain their significance.
Define Partial Differentiation and solve basic problems.
State and prove Euler's Theorem for Homogeneous Functions and explain its applications.
Define and explain the Total Derivative.
Define the Jacobian and discuss its properties.
Explain Functional Dependence and Independence using Jacobians.
Find the Jacobian of a given transformation.
Determine whether functions are functionally dependent or independent.
Find maxima and minima of functions of two variables and three variables.
Explain the Method of Lagrange Multipliers and solve constrained maxima and minima problems.
UNIT-5Define Double Integral and explain its evaluation in Cartesian coordinates.
Evaluate double integrals in Polar Coordinate System.
Explain the procedure for change of order of integration in Cartesian coordinates.
Explain change of variables for double integrals from Cartesian to polar coordinates using the Jacobian.
Define Triple Integral and explain its evaluation.
Evaluate triple integrals in Cartesian coordinates.
Explain change of variables for triple integrals from Cartesian to Cylindrical Coordinate System and Spherical Coordinate System.
Find the area of a plane region using double integrals.
Find the volume of a solid using triple integrals.
Compare Cartesian, polar, cylindrical, and spherical coordinate systems and state when each is most convenient.