Question

(PLEASE HELP ASAP)

Answer 1

9514 1404 393

Answer:

  A. 3×3

  B. [0, 1, 5]

  C. (rows, columns) = (# equations, # variables) for matrix A; vector x remains unchanged; vector b has a row for each equation.

Step-by-step explanation:

A. The matrix A has a row for each equation and a column for each variable. The entries in each column of a given row are the coefficients of the corresponding variable in the equation the row represents. If the variable is missing, its coefficient is zero.

This system of equations has 3 equations in 3 variables, so matrix A has dimensions ...

  A dimensions = (rows, columns) = (# equations, # variables) = (3, 3)

Matrix A is 3×3.

__

B. The second row of A represents the second equation:

  $0x_1+1x_2+5x_3=-1$

The coefficients of the variables are 0, 1, 5. These are the entries in row 2 of matrix A.

__

C. As stated in part A, the size of matrix A will match the number of equations and variables in the system. If the number of variables remains the same, the number of rows of A (and b) will reflect the number of equations. (The number of columns of A (and rows of x) will reflect the number of variables.)