Content location → MatricesEvidenceConnection evidence is not yet available in this language.
Content location → MatricesEvidenceA 2×2 matrix can be read column by column as two vectors in the plane. In the example A = [[3,1],[1,2]], the columns are (3,1) and (1,2), and these are drawn as arrows from the origin.
Content location → DeterminantsEvidenceFor the two real column vectors in standard Cartesian coordinates, the spanned parallelogram has area equal to the absolute determinant. The source notation |A| denotes the determinant itself. For this positive example, determinant and its absolute value both equal 5.
Content location → DeterminantsEvidenceConnection evidence is not yet available in this language.
Content location → Linear transformationsEvidenceConnection evidence is not yet available in this language.
Content location → Linear transformationsEvidenceWhen a 2x2 matrix acts as a transformation matrix, its columns represent the images of the standard unit vectors. The first column shows where [1, 0] lands, and the second column shows where [0, 1] lands.
Explanation → MatricesEvidenceConnection evidence is not yet available in this language.
Explanation → MatricesEvidenceA 2×2 matrix can be read column by column as two vectors in the plane. In the example A = [[3,1],[1,2]], the columns are (3,1) and (1,2), and these are drawn as arrows from the origin.
Explanation → MatricesEvidenceA 2×2 matrix can be read column by column as two vectors in the plane. In the example A = [[3,1],[1,2]], the columns are (3,1) and (1,2), and these are drawn as arrows from the origin.
Explanation → DeterminantsEvidenceFor the two real column vectors in standard Cartesian coordinates, the spanned parallelogram has area equal to the absolute determinant. The source notation |A| denotes the determinant itself. For this positive example, determinant and its absolute value both equal 5.
Explanation → DeterminantsEvidenceConnection evidence is not yet available in this language.
Content location → Interpreting determinants in terms of area | Matrices | Precalculus | Khan AcademyEvidenceFor the two real column vectors in standard Cartesian coordinates, the spanned parallelogram has area equal to the absolute determinant. The source notation |A| denotes the determinant itself. For this positive example, determinant and its absolute value both equal 5.
Explanation → DeterminantsEvidenceFor the two real column vectors in standard Cartesian coordinates, the spanned parallelogram has area equal to the absolute determinant. The source notation |A| denotes the determinant itself. For this positive example, determinant and its absolute value both equal 5.
Explanation → Linear transformationsEvidenceConnection evidence is not yet available in this language.
Explanation → Linear transformationsEvidenceWhen a 2x2 matrix acts as a transformation matrix, its columns represent the images of the standard unit vectors. The first column shows where [1, 0] lands, and the second column shows where [0, 1] lands.
Explanation → Linear transformationsEvidenceWhen a 2x2 matrix acts as a transformation matrix, its columns represent the images of the standard unit vectors. The first column shows where [1, 0] lands, and the second column shows where [0, 1] lands.
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