The transpose of a matrix is created by interchanging its rows and columns. The transpose of a matrix are denoted as \(A’\) or \(A^{\text{T}}\).
Notes
Questions & Solutions
\(\textbf{1)}\) Take the Transpose of this Matrix
\( \left[ {\begin{array}{ccc}21 & 22 & 23 \\41 & 42 & 43 \\81 & 82 & 83 \end{array} } \right]\)
\(\textbf{2)}\) Take the Transpose of this Matrix
\( \left[{\begin{array}{ccc} 1 \\ 2 \\ 5 \end{array} } \right]\)
\(\textbf{3)}\) Take the Transpose of this Matrix
\( \left[{\begin{array}{ccc} 6 & 7 \\ 3 & 8 \\ 9 & 0 \end{array} } \right]\)
\(\textbf{4)}\) Take the Transpose of this Matrix
\( \left[{\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array} } \right]\)
\(\textbf{5)}\) Take the Transpose of this Matrix
\( \left[{\begin{array}{c} 7 & -8 & 9 \end{array} } \right]\)
\(\textbf{6)}\) Take the Transpose of this Matrix
\( \left[{\begin{array}{c} 4 \end{array} } \right]\)
See Related Pages\(\)
\(\bullet\text{ Matrix Transpose Calculator (Symbolab.com)}\)
\(\bullet\text{ Intro to Matrices}\)
\(\,\,\,\,\,\,\,\,\)\(\left[ {\begin{array}{ccc}4 & -5 & 2 \\1 & 0 & 3 \\\end{array} } \right]\)
\(\bullet\text{ Matrix Operations}\)
\(\,\,\,\,\,\,\,\,\)\( \left[ {\begin{array}{ccc}3 & 45 & 6 \\-8 & 2 & 4 \\1 & 0 & 3 \\\end{array} } \right]\)\(+\left[ {\begin{array}{ccc}3 & 45 & 6 \\-8 & 2 & 4 \\1 & 0 & 3 \\\end{array} } \right]\)
\(\bullet\text{ Multiplying Matrices}\)
\(\,\,\,\,\,\,\,\,\)\(\left[{\begin{array}{cc} 1 & 2 \\ -3 & -4 \\\end{array} } \right]\)\(\left[ {\begin{array}{cc}6 & -3 \\5 & 0 \\\end{array} } \right]\)
\(\bullet\text{ Determinants}\)
\(\,\,\,\,\,\,\,\,\)\(\left|{\begin{array}{cc} a & b \\ c & d \\ \end{array} } \right|=ad-bc\)
\(\bullet\text{ Cramer’s Rule}\)
\(\,\,\,\,\,\,\,\,\text{ax+by=e } \& \text{ cx+dy=f}…\)
\(\bullet\text{ Identity Matrix}\)
\(\,\,\,\,\,\,\,\,\)\(\left[{\begin{array}{ccc} 1 & 0 & 0\\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]\)
\(\bullet\text{ Identity and Inverse Matrices}\)
\(\,\,\,\,\,\,\,\,A^{-1}=\displaystyle\frac{1}{ad-bc}\left[{\begin{array}{cc} a & b \\ c & d \\ \end{array} } \right]\)
\(\bullet\text{ Transpose Matrix}\)
\(\,\,\,\,\,\,\,\,\left[{\begin{array}{ccc} 1 \\ 2 \\ 5 \\ \end{array} } \right]\Rightarrow\left[{\begin{array}{c} 1 & 2 & 5 \end{array} } \right]\)
\(\bullet\text{ Rotation Matrix}\)
\(\,\,\,\,\,\,\,\,\)\(R(\theta)=\left[{\begin{array}{cc}\cos{\theta} & -\sin{\theta} \\\sin{\theta} & \cos{\theta} \\\end{array} } \right]\)
\(\bullet\text{ Eigenvectors and Eigenvalues}\)
\(\,\,\,\,\,\,\,\,(A-\lambda I)\vec{v}=\vec{0}\)
\(\bullet\text{ Andymath Homepage}\)
