Matrix Determinant Calculator
ANA›Life Services Authority›National Calculator Authority›Matrix Determinant Calculator
.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
Matrix Determinant Calculator
Calculate the determinant of a square matrix (2×2 up to 5×5) using cofactor expansion.
Matrix Size
2 × 2 3 × 3 4 × 4 5 × 5
Matrix Entries
Calculate Determinant
(function(){ / ── build grid ── / function matBuildGrid(){ var n = parseInt(document.getElementById('mat-size').value); var g = document.getElementById('mat-grid'); var html = ''; for(var r=0;r'; for(var c=0;c'; } html += ''; } html += ''; g.innerHTML = html; document.getElementById('mat-error').style.display='none'; document.getElementById('mat-result').style.display='none'; document.getElementById('mat-steps').style.display='none'; } window.matBuildGrid = matBuildGrid;
/ ── read matrix ── / function matRead(n){ var M=[]; for(var r=0;r'; if(n===2){ s+='det = ('+fmt(M[0][0])+')('+fmt(M[1][1])+') − ('+fmt(M[0][1])+')('+fmt(M[1][0])+')'; s+=' = '+fmt(M[0][0]M[1][1])+' − '+fmt(M[0][1]M[1][0])+''; s+=' = '+fmt(d)+''; } else if(n===3){ s+='Cofactor expansion along row 1:'; for(var c=0;c1'+(c+1)+' = ('+( sign>0?'+':'-')+'1)·'+fmt(M[0][c]) +'·['+fmt(minor[0][0])+'·'+fmt(minor[1][1])+'−'+fmt(minor[0][1])+'·'+fmt(minor[1][0])+']' +' = '+fmt(signM[0][c]md)+''; } s+='det = '+fmt(d)+''; } else { s+='det = '+fmt(d)+' (computed via recursive cofactor expansion)'; } return s; }
/ ── main calc ── / function matCalc(){ var errEl=document.getElementById('mat-error'); var resEl=document.getElementById('mat-result'); var stpEl=document.getElementById('mat-steps'); errEl.style.display='none'; resEl.style.display='none'; stpEl.style.display='none';
var n=parseInt(document.getElementById('mat-size').value); var M=matRead(n); if(!M){ errEl.textContent='All entries must be valid numbers.'; errEl.style.display='block'; return; } var d=det(M); var singular=Math.abs(d)det(A) = '+fmt(d)+'' +(singular?'⚠ The matrix is singular (det ≈ 0); it has no inverse.':''); resEl.style.display='block'; stpEl.innerHTML=matSteps(M,n,d); stpEl.style.display='block'; } window.matCalc = matCalc;
/ init / matBuildGrid(); })();
#### Formula
2×2: det(A) = a₁₁a₂₂ − a₁₂a₂₁
n×n (cofactor / Laplace expansion along row 1):
det(A) = Σj=1..n (−1)1+j · a1j · det(M1j)
where M1j is the (n−1)×(n−1) minor obtained by deleting row 1 and column j.
3×3 (Sarrus' rule): det(A) = a₁₁(a₂₂a₃₃−a₂₃a₃₂) − a₁₂(a₂₁a₃₃−a₂₃a₃₁) + a₁₃(a₂₁a₃₂−a₂₂a₃₁)
#### Assumptions & References
- The matrix must be square (n×n). Non-square matrices have no determinant.
- A determinant of 0 means the matrix is singular: it has no inverse and its rows/columns are linearly dependent.
- Reference: Lay, D.C. Linear Algebra and Its Applications, 5th ed., §3.1–3.2.
More Calculators
- Home Electrical Panel Capacity Calculator
- Pipe Insulation Thickness Calculator
- Water Damage Insurance Claim Cost Estimator
- Exterminator Visit Frequency Calculator
- Bye Week Impact Calculator
- Roster Roster Strength Calculator
- Strength of Schedule Calculator
- Refrigerant Charge Calculator — Superheat and Subcooling
- Heat Pump COP and Efficiency Calculator
- HVAC Filter Change Interval Calculator
- Airflow CFM Calculator — Fan and Ventilation Requirements
- SEER to EER Conversion Calculator — Efficiency Rating Comparison
Read Next
Study Time Planner Authority Network America › Life Services Authority › National Calculator Authority .calc-container { max-width: 640px;...