Linear Algebra

For what value of the parameter b will the following system of equations fail to have a unique solution? (HINT - Do not attempt to actually solve the equations!!!!) x+2by-z = 2 2bx+3y-bz = 3 x+2y+z = 0

Systems Of Equations : Cramer's Rule

Use Cramer's Rule to solve the following system of equations. -x+2y = 1 3x+2y -3z= -1 2y -3z = 2

Systems of Equations : Solve using Augmented Matrix

Solve the following system of equations by performing elementary row operations on the augmented matrix. x1-2x2 +2x4 = 6 2x1-4x2+x3-x4 =-2 3x1+6x2-x3-x4=-4 x1-2x2+x3-3x4=-8

Linear Algebra : Inverse of Matrix

Compute the inverse of the matrix below? 3 -1 -3 6 0 -2 -4 -1 3

System of Equations: Solve using Inverse of Coefficient Matrix

Solve the following system of equations by computing the inverse of the coefficient matrix. -x+2y =4 2x-y+2z = -2 2y-z = 4

Linear Algebra : Matrix Proof

Prove that if ; A is a 2x2 matrix then A2-Tr(A)A+Det(A)I=0.

Linear Algebra : Inverse and Product of Elementary Matrices

Compute the inverse of matrix A below, and use this to express A as a product of elementary matrices 2 0 1 A= 0 1 1 1 -1 0

Linear Algebra : Homogeneous Equation

Let A be a 3x3 matrix such that At=-A(i.e.,A is a skew - symmetric). Find the general solution of the homogeneous equation Ax=0.

Linear Algebra : Adjoint and Inverse

Compute the adjoint of the matrix A below, and use this to compute the inverse of A. 2 0 4 A= 2 1 0 0 0 1

Linear Algebra : Adjoint and Inverse

Compute the adjoint of the matrix A below, and use this to compute the inverse of A. 2 0 4 A= 2 1 0 0 0 1