1 Systems Of Linear Equations 2 Matrices 3 Determinants 4 Vector Spaces 5 Inner Product Spaces 6 Linear Transformations 7 Eigenvalues And Eigenvectors A Appendix Chapter3: Determinants
3.1 The Determinants Of A Matrix 3.2 Determininants And Elementary Operations 3.3 Properties Of Determinants 3.4 Applications Of Determinants 3.CR Review Exercises 3.CM Cumulative Review Section3.CM: Cumulative Review
Problem 1CM Problem 2CM Problem 3CM: In Exercises 3and4, use Gaussian elimination to solve the system of linear equations. x2y=53x+y=1 Problem 4CM: In Exercises 3and4, use Gaussian elimination to solve the system of linear equations.... Problem 5CM: Use a software program or a graphing utility to solve the system of linear equations.... Problem 6CM Problem 7CM: Solve the homogeneous linear system corresponding to the coefficient matrix. [121200242412] Problem 8CM: Determine the values of k such that the system is consistent. x+2yz=3xy+z=2x+y+z=k Problem 9CM: Solve for x and y in the matrix equation 2AB=I, given A=[1123] and B=[x2y5]. Problem 10CM: Find ATA for the matrix A=[531246]. Show that this product is symmetric. Problem 11CM: In Exercises 11-14, find the inverse of the matrix if it exists. [2346] Problem 12CM: In Exercises 11-14, find the inverse of the matrix if it exists. [2336] Problem 13CM Problem 14CM: In Exercises 11-14, find the inverse of the matrix if it exists. [110365010] Problem 15CM: In Exercises 15 and 16, use an inverse matrix to solve the system of linear equations. x+2y=03x6y=8 Problem 16CM: In Exercises 15 and 16, use an inverse matrix to solve the system of linear equations. 2xy=62x+y=10 Problem 17CM: Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410] Problem 18CM: Find the determinant of the matrix. [4032013501511103] Problem 19CM: Find a |A|, b |B|, c AB and d |AB| then verify that |A||B|=|AB|. A=[1342], B=[2105] Problem 20CM: Find a |A| and b |A1| A=[523104682] Problem 21CM: If |A|=7 and A is of order 4. Then find each determinant. a |3A| b |AT| c |A1| d |A3| Problem 22CM: Use the adjoint of A=[151021102] to find A1 Problem 23CM: Let X1,X2,X3 and b be the column matrices below. X1=[101], X2=[110], X3=[011] and b=[123] Find... Problem 24CM: Use a system of linear equation to find the parabola y=ax2+bx+c that passes through the points... Problem 25CM: Use a determinant to find an equation of the line passing through the points (1,4) and (5,2) Problem 26CM: Use a determinant to find the area of the triangle with vertices (2,2), (8,2) and (6,5) Problem 27CM: Determine the currents I1I2 and I3 for the electric network shown in the figure at the left. Problem 28CM: A manufacture produce three models of a product and ships them to two warehouse. In the matrix... Problem 29CM Problem 24CM: Use a system of linear equation to find the parabola y=ax2+bx+c that passes through the points...
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Solve for the linear equation of the plane through the origin and perpendicular to the vector ⟨−4,−5,3⟩.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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