7. Systems of Equations & Matrices

Introduction to Matrices

Open Question
In Exercises 21–38, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
Open Question
In Exercises 1–8, write the augmented matrix for each system of linear equations.
Multiple Choice
Write the equations in standard form, then represent the system using an augmented matrix.
$3x+5y-9=0$
$8x=-4y+3$
Multiple Choice
Perform the indicated Row Operation.
SWAP $R_1\leftrightarrow R_2$
Multiple Choice
Perform the indicated Row Operation.
ADD $R_1+2\cdot R_3\rightarrow R_1$
Multiple Choice
Solve the system of equations by using row operations to write a matrix in REDUCED row-echelon form.
$4x+2y+3z=6$
$x+y+z=3$
$5x+y+2z=5$
Multiple Choice
Write the system of equations represented by the augmented matrix shown.
Open Question
In Exercises 1–2, perform each matrix row operation and write the new matrix.
Open Question
How many rows and how many columns does this matrix have? What is its dimension? <4x2 Matrix>
Open Question
In Exercises 1 - 4,a. Give the order of each matrix,b. If A = [a_ij], identify a_32 and a_23, or explain why identification is not possible,4 - 7 5- 6 8 - 1(please enclose the values above in a matrix symbol)
Open Question
In Exercises 1–8, write the augmented matrix for each system of linear equations.
Open Question
In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
Open Question
What is the augmented matrix of the following system? -3x + 5y = 2 6x + 2y = 7
Open Question
In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
Open Question
In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.