Euclidean spaces Last updated Mar 3, 2020 Page ID22648 Save as PDF ur la 23 5.pg Basis and dimension Basis and dimension4.2.11.pg4.2.12.pg4.2.14.pg4.2.15.pg4.2.17 21a.pg4.2.18.pg4.2.19.pg4.2.20.pg4.2.21.pg4.2.23.pg4.2.25.pg4.2.27.pg4.2.41.pg4.2.41 47a.pg4.2.47.pg4.2.48.pg4.2.48 54a.pg4.2.5.pg4.2.50.pg4.2.51.pg4.2.52.pg4.2.53.pg4.2.54.pg4.2.6.pg4.2.64.pg4.2.65.pg4.2.72.pg4.2.73.pg4.2.8.pgBasis 01a.pgBasis 01b.pgBasis 02a.pgBasis 02b.pgBasis 03a.pgBasis 03b.pgBasis 04a.pgBasis 04b.pgBasis 05a.pgBasis 05b.pgexpandBasis.pgGraphical 02.pgproblem5.pgproblem6.pgproblem7.pgproblem8.pgproblem9.pgSpan ind 01.pgSpan ind 02.pgSpan ind 03.pgSpan ind 04.pgur la 10 1.pgur la 10 23.pgur la 10 24.pgur la 10 25.pgur la 10 26.pgur la 10 32.pgur la 9 11.pgur la 9 12.pgur la 9 13.pgShow allCoordinate vectors and change of basisChange of basis 01.pgChange of basis 02.pgCoord vector 01.pgCoord vector 02.pgGeom basis change 01.pgGeom basis change 02.pgGeom basis change 03.pgGeom lin trans 04.pgGeom lin trans 05.pgguessCoordinates.pgR2BasisTrans.pgur la 10 2.pgur la 10 3.pgur la 10 4.pgur la 10 5.pgShow allLinear combinations2.1.15.pg2.1.17.pg2.1.19.pg2.1.27.pg2.1.28.pg2.1.29.pg2.1.4.pg2.1.49.pg2.1.50.pg2.1.52.pg2.1.53.pg2.1.6.pg2.1.64.pgguessCoefficients.pgLin combi 01a.pgLin combi 01b.pgLin combi 02a.pgLin combi 02b.pgLin combi 03a.pgLin combi 03b.pgLin combi 04a.pgLin combi 04b.pgLin combi 05a.pgLin combi 05b.pgLin combi 06a.pgLin combi 06b.pgLin combi 07a.pgLin combi 07b.pgproblem2.pgproblem3.pgproblem4.pgproblem5.pgur la 8 10.pgur la 8 8.pgur la 9 10.pgShow allLinear independence2.3.10.pg2.3.11.pg2.3.13.pg2.3.14.pg2.3.16.pg2.3.17.pg2.3.19.pg2.3.2.pg2.3.20.pg2.3.21.pg2.3.22.pg2.3.23.pg2.3.24.pg2.3.29.pg2.3.3.pg2.3.39.pg2.3.4.pg2.3.40.pg2.3.41.pg2.3.42.pg2.3.43.pg2.3.44.pg2.3.5.pg2.3.68.pg2.3.69.pg2.3.7.pg2.3.73.pg2.3.8.pg2.3.9.pgDep 01a.pgDep 01b.pgDep 02a.pgDep 02b.pgDep 04.pgDep 05.pgGraphical 01.pgInd 01a.pgInd 01b.pgInd 03.pgproblem10.pgproblem11.pgproblem3.pgproblem4.pgproblem5.pgproblem8.pgprob 1.pgprob 4.pgprob 5.pgur la 9 1a.pgur la 9 3.pgur la 9 3a.pgur la 9 7.pgur la 9 9.pgShow allRow, column, and null spaces4.1.22.pg4.1.23.pg4.1.27.pg4.1.28.pg4.1.30.pg4.1.46.pg4.1.47.pg4.1.77.pg4.1.80.pg4.2.29.pg4.2.29a.pg4.2.30a.pg4.2.32a.pg4.3.1.pg4.3.14.pg4.3.15.pg4.3.23.pg4.3.24.pg4.3.3.pg4.3.30.pg4.3.34.pg4.3.4.pg4.3.43.pg4.3.43 52a.pg4.3.46.pg4.3.47.pg4.3.5.pg4.3.6.pgBasis 10.pgBasis 10 null space.pgBasis 11.pgBasis 11 column space.pgBasis 12.pgBasis 12 row space.pgBasis 13.pgBasis 13 null space.pgBasis 14.pgBasis 14 column space.pgBasis 15.pgBasis 15 null space.pgBasis 16.pgBasis 16 row space.pgBasis 17.pgBasis 17 row space.pgBasis 18.pgBasis 18 column space.pgBasis 19.pgBasis 19 column space.pgBasis 30.pgBasis 31.pgproblem1.pgproblem10.pgproblem16.pgproblem2.pgproblem3.pgproblem6.pgproblem7.pgproblem8.pgproblem9.pgur la 10 11a.pgur la 10 13a.pgur la 10 15a.pgur la 10 28.pgur la 10 29.pgur la 10 30.pgur la 10 31.pgShow allSpan2.2.10.pg2.2.11.pg2.2.2.pg2.2.21.pg2.2.22.pg2.2.23.pg2.2.24.pg2.2.26.pg2.2.28.pg2.2.29.pg2.2.30.pg2.2.31.pg2.2.32.pg2.2.35.pg2.2.37.pg2.2.39.pg2.2.4.pg2.2.40.pg2.2.41.pg2.2.42.pg2.2.51.pg2.2.52.pg2.2.53.pg2.2.54.pg2.2.55.pg2.2.56.pg2.2.57.pg2.2.58.pg2.2.59.pg2.2.60.pg2.2.7.pg2.2.77.pg2.2.8.pg2.3.26.pg2.3.28.pg2.3.30.pg2.3.72.pgguessDependent.pgproblem1.pgproblem10.pgproblem13.pgproblem2.pgproblem3.pgproblem4.pgproblem5.pgproblem6.pgproblem7.pgproblem8.pgproblem9.pgur la 9 8.pgShow allSubspaces4.1.11.pg4.1.12.pg4.1.16.pg4.1.3.pg4.1.45.pg4.1.50 58a.pg4.1.51.pg4.1.52.pg4.1.53.pg4.1.58.pg4.1.6.pg4.1.7.pg4.1.73.pg4.1.75.pg4.1.9.pgproblem3.pgproblem4.pgproblem5.pgSubspaces nonempty 01.pgSubspaces nonempty 02.pgSubspaces nonempty 03.pgSubspaces nonempty 04.pgSubspaces nonempty 05.pgSubspaces nonempty 06.pgSubspaces nonempty 07.pgSubspaces nonempty 08.pgSubspaces zero 01.pgSubspaces zero 02.pgSubspaces zero 03.pgSubspaces zero 04.pgSubspaces zero 05.pgSubspaces zero 06.pgSubspaces zero 07.pgSubspaces zero 08.pgur la 8 6.pgShow allVectors2.1.66.pg2.1.68.pg2.1.69.pg2.1.70.pg2.1.71.pg2.1.72.pgvectorOperations.pgvectorOperations2.pgvectorOperations3.pgShow all