Math Lab

 Today I will write about Math Lab.Math Lab is very important in mathematics.Today's blog will show the experiments of Matrix.So let's get started

Matrix: Suppose (1,2) and (3,4) are the two components of the matrix. Then the matrix structure will be:

      A={{1,2},{3,4}}//MatrixForm

  

TagBox[RowBox[{"(", "\:2060", GridBox[{{ItemBox["1"], ItemBox["2"]}, {ItemBox["3"], ItemBox["4"]}}, RowSpacings -> 1, ColumnSpacings -> 1, RowAlignments -> Baseline, ColumnAlignments -> Center], "\:2060", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]

Again the transpose matrix will be -

Trans=Transpose[{{1,2},{3,4}}]//MatrixForm

TagBox[RowBox[{"(", "\:2060", GridBox[{{ItemBox["1"], ItemBox["3"]}, {ItemBox["2"], ItemBox["4"]}}, RowSpacings -> 1, ColumnSpacings -> 1, RowAlignments -> Baseline, ColumnAlignments -> Center], "\:2060", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]

The value of the judge will be -

Det[{{1,2},{3,4}}]

Out:-2 

Eigenvalues will be–

In[25]:= e1=Eigenvalues[{{1,2},{3,4}}]

Out[25]= {FractionBox["1", "2"] (5+SqrtBox["33"]),FractionBox["1", "2"] (5-SqrtBox["33"])}

e1[[2]]

FractionBox["1", "2"] (5-SqrtBox["33"])

Trace of the matrix will be–

In[18]:= Tr[{{1,2},{3,4}}]

Out[18]= 5

Inverse of the matrix will be–

In[20]:= Inverse[{{1,2},{3,4}}]

Out[20]= {{-2,1},{FractionBox["3", "2"],-FractionBox["1", "2"]}}

The value of Eigenvectors of the matrix will be–

In[24]:= Eigenvectors[{{1,2},{3,4}}]

Out[24]= {{FractionBox["1", "6"] (-3+SqrtBox["33"]),1},{FractionBox["1", "6"] (-3-SqrtBox["33"]),1}}