How to do Matrix Multiplication and display in LaTex

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This video demonstrates the rule for Matrix multiplication, then shows how to find the determinant , and a special rule for determinants. ad-bc= det A • • Find Eigenvalues and Eigenvectors • • Find the Determinant of 3x3 Matrix • • how to find the Inverse of 2 by 2 Mat... • • Solve equations with 3 variables usin... • • Long Division of a polynomial with 2 ... • \\documentclass[a4,paper,10pt]{article} • \\usepackage{fancyhdr} • \\usepackage{amsmath} • \\usepackage{amssymb} • \\usepackage{graphicx} • \\usepackage{xfrac} • \\usepackage{gensymb} • \\usepackage{polynom} • \\usepackage{scalerel} • \\usepackage{stackengine} • \\usepackage{xcolor} • \\usepackage{bigints} • \\usepackage{physics} • \\usepackage{lastpage} • \\pagestyle{fancy} • \\fancyhf{} • \\lhead{Matrices} • \\chead{Sum Chief} • \ head{YouTube Demo} • \ foot{Page \\thepage\\ of \\pageref{LastPage}} • \\title{} • \\setcounter{page}{1} • • • \\begin{document} • \\begin{enumerate} • \\item[(a)] • Show $\\textbf{K}\\times \\textbf{H}$ • \\[ • \\textbf{H}= \\left( \\begin{array}{cc} • 1 3 \\\\ • 1 1 \\\\ • \\end {array}\ ight) • \\textbf{K}= \\left( \\begin{array}{cc} • 1 2 \\\\ • 5 6 \\\\ • \\end {array}\ ight) • \\] • \\[ • = \\left( \\begin{array}{cc} a b \\\\ c d \\\\ \\end {array}\ ight) \\times \\left( \\begin{array}{cc} e f \\\\ g h \\\\ \\end {array}\ ight) • \\] • \\[ • = \\left( \\begin{array}{cc} (a\\times e+b\\times g) (a\\times f+b\\times h) \\\\ (c\\times e+d\\times g) (c\\times f + d\\times h) \\\\ \\end {array}\ ight) • \\] • \\[ • \\left( \\begin{array}{cc} 1 2 \\\\ 5 6 \\\\ \\end {array}\ ight) • \\times \\left( \\begin{array}{cc} 1 3 \\\\ 1 1 \\\\ \\end {array}\ ight) • = \\left( \\begin{array}{cc} (1\\times1 +2\\times 1) (1\\times3+2\\times 1) \\\\ (5\\times1+6\\times1) (5\\times 3+6\\times 1) \\\\ \\end {array}\ ight) • \\] • \\[ • \\text{which gives } \\left( \\begin{array}{cc} 3 5 \\\\ 11 21 \\\\ \\end {array}\ ight) • \\] • we shall calll this matrix \\textbf{A} • \\[ • \\textbf{A}= \\left( \\begin{array}{cc} • 3 5 \\\\ • 11 21 \\\\ • \\end {array}\ ight) • \\] • The determinant is $ad-bc$.\\\\ • \\[ • \\textbf{A}= \\left( \\begin{array}{cc} • a b \\\\ • c d \\\\ • \\end {array}\ ight) • \\] • \\[3\\times21-5\\times 11=8\\] • The determinant multiplication rule. • \\[ • \\abs{\\textbf{H}}\\times\\abs{\\textbf{K}}=\\abs{\\textbf{K}\\times\\textbf{H}}\\\\ • \\] • • \\clearpage • • • • \\[ • \\textbf{A}= \\left( \\begin{array}{cc} • 3 5 \\\\ • 11 21 \\\\ • \\end {array}\ ight) • \\] • The determinant is $ad-bc$.\\\\ • \\[ • \\textbf{A}= \\left( \\begin{array}{cc} • a b \\\\ • c d \\\\ • \\end {array}\ ight) • \\] • \\[3\\times21-5\\times 11=8\\] • • The inverse is shown as • \\begin{align*} • \\textbf{A}^{-1}= \\frac{1}{\\abs{det}} \\left( \\begin{array}{cc}d -b \\\\-c a \\\\\\end {array}\ ight)\\\\ • \\\\ • = \\frac{1}{\\abs{A}} \\left( \\begin{array}{cc}3 5 \\\\11 21 \\\\\\end {array}\ ight)\\\\ • \\\\ • = \\frac{1}{8} \\left( \\begin{array}{cc}21 -5 \\\\-11 3 \\\\\\end {array}\ ight)\\\\ • \\\\ • \\textbf{A}^{-1}= \\left( \\begin{array}{cc}\\sfrac{21}{8} -\\sfrac{5}{8} \\\\-\\sfrac{11}{8} \\sfrac{3}{8} \\\\\\end {array}\ ight)\\\\ • \\end{align*} • • to prove an inverse is correct multiply by the original.\\\\ • $\\textbf{A}\\times\\textbf{A}^{-1}=\\textbf{I}$ • \\[ • \\left( \\begin{array}{cc} 3 5 \\\\ 11 21 \\\\ \\end {array}\ ight) • \\times \\left( \\begin{array}{cc} \\sfrac{21}{8} -\\sfrac{5}{8} \\\\-\\frac{11}{8} \\sfrac{3}{8} \\\\ \\end {array}\ ight) • \\] • \\[ • = \\left( \\begin{array}{cc} \\left[\\cfrac{3\\times21}{8}+\\cfrac{5\\times-11}{8}\ ight] \\left[\\cfrac{3\\times-5}{8}+\\cfrac{5\\times3}{8}\ ight] \\\\ \\left[\\cfrac{11\\times21}{8}+\\cfrac{21\\times-11}{8}\ ight] \\left[\\cfrac{11\\times-5}{8}+\\cfrac{21\\times3}{8}\ ight] \\\\ \\end {array}\ ight) • \\] • \\[ • \\left( \\begin{array}{cc} 1 0 \\\\ 0 1 \\\\ \\end {array}\ ight) =\\textbf{I} • \\] • • • \\end{enumerate} • \\end{document}

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