Solve matrix equation Ax=b

 

11: Solve matrix equation Ax=b

Solve Ax=b (and check the solution) given that

A =

1   2   0
2   5  -1
4  10  -1

b =

7
8
9

Mathematica:

A = { {1,2,0}, {2,5,-1}, {4,10,-1} }
b = {7,8,9}
x = LinearSolve[ A, b ]
A . x     (does equal b)

Matlab:

A = [ 1 2 0 ; 2 5 -1 ; 4 10 -1 ]
b = [ 7 8 9 ]
x = A\transpose(b)
A * x     (does equal b)

Maple:

xxx

IDL:

A = [ [1,2,0], [2,5,-1], [4,10,-1] ]
b = [7,8,9]
svd, transpose(A), w,u,v
svbksb, u,w,v,b,x
print, x
print, x # A   (does equal b)

 

 

>> help('\')
\   Backslash or left matrix divide.
    A\B is the matrix division of A into B, which is roughly the
    same as INV(A)*B , except it is computed in a different way.
    If A is an N-by-N matrix and B is a column vector with N
    components, or a matrix with several such columns, then
    X = A\B is the solution to the equation A*X = B. A warning
    message is printed if A is badly scaled or nearly singular.
    A\EYE(SIZE(A)) produces the inverse of A.
    If A is an M-by-N matrix with M < or > N and B is a column
    vector with M components, or a matrix with several such columns,
    then X = A\B is the solution in the least squares sense to the
    under- or overdetermined system of equations A*X = B. The
    effective rank, K, of A is determined from the QR decomposition
    with pivoting. A solution X is computed which has at most K
    nonzero components per column. If K < N this will usually not
    be the same solution as PINV(A)*B.  A\EYE(SIZE(A)) produces a
    generalized inverse of A.
    C = mldivide(A,B) is called for the syntax 'A \ B' when A or B is an
    object.
    See also ldivide, rdivide, mrdivide.

    Overloaded methods:
       sym/mldivide
       StaticModel/mldivide
       DynamicSystem/mldivide
       timeseries/mldivide

    Reference page in Help browser
       doc mldivide