Chapter 4, General Vector Spaces Section 4.1, Real Vector Spaces
... (a) If A and B are n × m matrices then A+B is also a n × m matrix (b) A+B=B+A (c) A+(B+C)=(A+B)+C (d) There is zero matrix 0, such that A+0=0+A=A (e) For each matrix A we have -A such that A+(-A)=0 (f) If k is any real scalar, then kA is in V (g) k(A+B)=kA+kB (h) (k+m)A=kA+mA (i) k(mA)=(km)A (j) 1A= ...
... (a) If A and B are n × m matrices then A+B is also a n × m matrix (b) A+B=B+A (c) A+(B+C)=(A+B)+C (d) There is zero matrix 0, such that A+0=0+A=A (e) For each matrix A we have -A such that A+(-A)=0 (f) If k is any real scalar, then kA is in V (g) k(A+B)=kA+kB (h) (k+m)A=kA+mA (i) k(mA)=(km)A (j) 1A= ...
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