MATH 129A
Chapter 1 Summary
Sept. 17, 2015
1. Define each term (a) – (m), then match with all terms (i) – (vii) to which it relates.
(a)Solution set /Particular solution
(i)vector
(b)Equivalent
(ii)matrix
(c)Consistent/Inconsistent
(iii)system of linear equations
(d)Coefficient matrix/Augmented matrix
(iv)set of vectors
(e)Echelon form/Reduced echelon form
(v)matrix equation
(f)Pivot column/Pivot position/Pivot
(vi)matrix columns
(g)Basic/Free variables
(vii)vector equation
(h)Linear combination/Span/Spanning set
(vii)scalar
(i)Homogeneous/Trivial solution
(j)Parametric form/Parametric vector form
(k)Linearly independent/Dependent/Linear dependence relation
(l)Linear transformation/Matrix transformation/Standard matrix
(m)Difference equation
2. What properties must matrix A have in order for the following to hold? List ALL properties of which
you can think.
Ax  0
Ax  b
has only the trivial solution
has a solution for every b
Ax  0
is consistent
Ax  b
Ax  0
has a unique solution for every b
has the trivial solution
Ax  b
has many solutions for every b
Ax  b does not have a solution for any b
T(x)  Ax is one - to - one
T(x)  Ax is onto
T(x)  Ax is one - to - one and onto