m=(({{1, 5}, {2, 1}}))

m.{x,y}=={a,b}

Solve[%,{x,y}]

LinearSolve[m,{a,b}]

n:=LinearSolve[m]
n[{a,b}]

LinearSolve[m][{a,b}]

Inverse[m].{a,b}

RowReduce[{{1,5,a},{2,1,b}}]//MatrixForm

NullSpace[m]

m1 = {{1,2,3},{4,5,6},{7,8,9}}

NullSpace[m1]

MatrixRank[m1]

m1.{1,-2,1}

m2=(({{2, -1, 1}, {3, 1, -1}, {1, 2, 1}}));
b2={3,2,-4};
xx={x,y,z};

m2.xx==b2;
Solve[%,xx]

Inverse[m2].b2

LinearSolve[m2,b2]

n1:=LinearSolve[m2]
n1[b2]

RowReduce[{{2,-1,1,3},{3,1,-1,2},{1,2,1,-4}}]//MatrixForm

f[x_]=Sin[x]/x;
Plot[f[x],{x,-2Pi,2Pi}]

Limit[f[x],x->0]

Limit[f[x],x->Infinity]

Clear[g]
g[x_]=(x^3-1)^(4/3)(x-1)^-1

Plot[g[x],{x,0.5,1.4},PlotRange->{-2,5}]

Limit[g[x],x->1]

Clear[g1]
g1[x_]=((x^3-1)^4)^(1/3)(x-1)^-1

Plot[g1[x],{x,0.5,1.4},PlotRange->{-2,5}]

Limit[g[x],x->1]

f1[x_]=(2x +Abs[x])/Abs[x] Cos[x];
Plot[f1[x],{x,-5,5}]

Limit[f1[x],x->0,Direction->1]

Limit[f1[x],x->0,Direction->-1]

Limit[f1[x],x->0]

Clear[f,g]
f[x_]=1/(x-1);
g[x_]=1/(1-x)^2;
Plot[f[x],{x,-2,4}]
Plot[g[x],{x,-2,4}, PlotRange->{0,30}]

{Limit[f[x],x->1,Direction->1],Limit[f[x],x->1,Direction->-1]}

{Limit[g[x],x->1,Direction->1],Limit[g[x],x->1,Direction->-1]}