maths.free › Linear Algebra › Determinants

Determinants

2×2 by ad − bc, larger by cofactor expansion, and what the number means.

The determinant of a matrix is the factor by which it scales area (2×2) or volume (3×3), with a sign for orientation. A zero determinant means the matrix squashes space flat and cannot be inverted. The 3D view draws the column vectors and the box they span.

Contoh soal · det [[1,2],[3,4]]

Linear-Algebra · Determinants

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

\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]

Langkah demi langkah

  1. \det\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]

    Determinant of a 2×2 matrix.

  2. = (1)(4) - (2)(3)

    For 2×2: ad − bc.

  3. \det A = -2

    Result.

Tampilkan jawaban
\det A = -2

Sekarang Anda Pilih soal, atau ketik atau gambar soal Anda sendiri. Setiap langkah, sebuah gambar, jawabannya tersembunyi sampai Anda memintanya.

Simpan pekerjaan Anda sendiri

Sebuah akun gratis menambahkan catatan pada setiap pelajaran, catatan apa yang telah Anda selesaikan, masalah yang Anda selesaikan di satu tempat, dan tutor yang dapat Anda tanyakan tentang halaman ini. matematika itu sendiri terbuka untuk semua orang, ditandatangani atau tidak.

Daftar Masuk

Simbol yang digunakan di sini

Sentuh simbol apapun untuk definisi lengkap, gambar, dan apa setiap huruf di dalamnya berarti.

Bagaimana: Determinants

  1. Determinant of a 2×2 matrix.
  2. For 2×2: ad − bc.
  3. Result.

Pertanyaan yang sering diajukan

What does a determinant mean geometrically?

It is the factor by which the matrix scales area (2×2) or volume (3×3), with a negative sign if orientation flips. Zero means the matrix flattens space and cannot be undone.

What is an eigenvector?

A direction the matrix does not turn: it only stretches it by the eigenvalue. Along eigenvectors a complicated matrix acts like multiplication by a number.

Why is matrix multiplication not commutative?

Because a matrix is a transformation and AB means "do B, then A". Rotating then reflecting is not the same as reflecting then rotating.

Lainnya di Linear Algebra

Matrix inverseEigenvalues and eigenvectorsMatrix multiplicationRow reductionVector spaces, span and linear independenceOrthogonality, projections and least squaresDiagonalisation and matrix powersLinear transformations and change of basis