Chapter 1 Definitions

Question 1

Definition of a Linear Equation in n Variables

Answer 1

a1x1 + a2x2 + … + anxn = b

Question 2

Definition of a Matrix

Answer 2

[ a11 a12 a13 ... a1n]
[a21 a22 a23 ... a2n]
[a31 a32 a33 ... a3n]
[.      .       .       .        ]
[am1 am2 am3 amn]

Question 3

Elementary Row Operations

Answer 3

1) interchange two rows
2) multiply a row by a nonzero constant
3) add a multiple of a row to another row

Question 4

row-echelon form

Answer 4

1) row entirely of zeros at bottom
2) each row not zeros, first nonzero entry is 1
3) two successive rows, the leading 1 in the higher row is farther to the left than the leading 1 in the lower row

Question 5

Number of Solutions of a Homogeneous system

Answer 5

every homogeneous system of linear equations is consistent. if the system has fewer equations than variables, then it must have infinitely many

Question 6

Consistent system of equations

Answer 6

contains at least one solution