restart; with(LinearAlgebra): a:=Vector([1,1,0,0]); b:=Vector([0,1,1,0]): c:=Vector([0,0,1,1]): LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJhR0YoS0knUlRBQkxFR0YoNiUiNVtsZWQ8OilbJCpvJC1JJ01BVFJJWEdGKDYjNyY3Iy1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMUYoRjY3Iy1GODYjUSIwRihGPiZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRihGKDcjLUZCNiMvSSQlaWRHRihGMQ== A:=Matrix(<a|b|c|a-b|b-c|a-c>); #A:=Matrix([[1,0,0,1,0,1],[1,1,0,0,1,1],[0,1,1,-1,0,-1],[0,0,1,0,-1,-1]]); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoS0knUlRBQkxFR0YoNiUiNScqKlwoUj46KVskKm8kLUknTUFUUklYR0YoNiM3JjcoLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoRj5GN0Y+Rjc3KEY3RjdGPkY+RjdGNzcoRj5GN0Y3LUY4NiNRKyZ1bWludXMwOzFGKEY+RkM3KEY+Rj5GN0Y+RkNGQ0knTWF0cml4R0YlRig3Iy1GRzYjL0kkJWlkR0YoRjE= LUDecomposition(A); 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
<Text-field style="Heading 1" layout="Heading 1">R^4</Text-field> CA:=ColumnSpace(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNDQUdGKDclS0knUlRBQkxFR0YoNiUiNSNISyhSPjopWyQqbyQtSSdNQVRSSVhHRig2IzcmNyMtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKDcjLUY5NiNRIjBGKEY/RjcmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoRihLRjA2JSI1N0N0Uj46KVskKm8kLUY0NiM3JkY/RjdGPzcjLUY5NiNRKyZ1bWludXMwOzFGKEZDRihLRjA2JSI1S0R0Uj46KVskKm8kLUY0NiM3JkY/Rj9GN0Y3RkNGKDcjNyUtRkM2Iy9JJCVpZEdGKEYyLUZDNiMvRmZuRkktRkM2Iy9GZm5GUw== NTA:=NullSpace(Transpose(A)); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSROVEFHRig8I0tJJ1JUQUJMRUdGKDYlIjVnXXNSPjopWyQqbyQtSSdNQVRSSVhHRig2IzcmNyMtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRKyZ1bWludXMwOzFGKDcjLUY5NiNRIjFGKEY3Rj8mSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoRig3IzwjLUZDNiMvSSQlaWRHRihGMg==
<Text-field style="Heading 1" layout="Heading 1">R^6</Text-field> RA:=RowSpace(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNSQUdGKDclS0knUlRBQkxFR0YoNiUiNSUpKT4oUj46KVskKm8kLUknVkVDVE9SR0YoNiM3KC1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMUYoLUY4NiNRIjBGKEY+RjdGPkY3JkknVmVjdG9yR0YlNiNJJHJvd0dGKEYoS0YwNiUiNS8rc1I+OilbJCpvJC1GNDYjNyhGPkY3Rj4tRjg2I1ErJnVtaW51czA7MUYoRjdGPkZBRihLRjA2JSI1QyxzUj46KVskKm8kLUY0NiM3KEY+Rj5GN0Y+RktGS0ZBRig3IzclLUZBNiMvSSQlaWRHRihGMi1GQTYjL0ZZRkctRkE2Iy9GWUZQ NA:=NullSpace(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNOQUdGKDwlS0knUlRBQkxFR0YoNiUiNXNGclI+OilbJCpvJC1JJ01BVFJJWEdGKDYjNyg3Iy1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1ErJnVtaW51czA7MUYoNyMtRjk2I1EiMEYoNyMtRjk2I1EiMUYoRj9GP0ZDJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKEYoS0YwNiUiNTdJclI+OilbJCpvJC1GNDYjNyhGP0Y3RkNGP0ZDRj9GR0YoS0YwNiUiNV9LclI+OilbJCpvJC1GNDYjNyhGN0ZDRj9GQ0Y/Rj9GR0YoNyM8JS1GRzYjL0kkJWlkR0YoRjItRkc2Iy9GZm5GTS1GRzYjL0ZmbkZT
<Text-field style="Heading 1" layout="Heading 1">C.R</Text-field> C:=Transpose(Matrix([[1,1,0,0],[0,1,1,0],[0,0,1,1]])); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJDR0YoS0knUlRBQkxFR0YoNiUiNWMuclI+OilbJCpvJC1JJ01BVFJJWEdGKDYjNyY3JS1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMUYoLUY4NiNRIjBGKEY+NyVGN0Y3Rj43JUY+RjdGNzclRj5GPkY3SSdNYXRyaXhHRiVGKDcjLUZENiMvSSQlaWRHRihGMQ== R:=Matrix([[1,0,0,1,0,1],[0,1,0,-1,1,0],[0,0,1,0,-1,-1]]); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoS0knUlRBQkxFR0YoNiUiNT9bcVI+OilbJCpvJC1JJ01BVFJJWEdGKDYjNyU3KC1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMUYoLUY4NiNRIjBGKEY+RjdGPkY3NyhGPkY3Rj4tRjg2I1ErJnVtaW51czA7MUYoRjdGPjcoRj5GPkY3Rj5GQkZCSSdNYXRyaXhHRiVGKDcjLUZGNiMvSSQlaWRHRihGMQ== C.R; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSdSVEFCTEVHRig2JSI1LytxUj46KVskKm8kLUknTUFUUklYR0YoNiM3JjcoLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjY2I1EiMEYoRjxGNUY8RjU3KEY1RjVGPEY8RjVGNTcoRjxGNUY1LUY2NiNRKyZ1bWludXMwOzFGKEY8RkE3KEY8RjxGNUY8RkFGQUknTWF0cml4R0YlRig3Iy1GRTYjL0kkJWlkR0YoRi8=
<Text-field style="Heading 1" layout="Heading 1">QR decomposition</Text-field> QRDecomposition(A); 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