- #1
PcumP_Ravenclaw
- 106
- 4
I have some doubts about the solution to ## x + (x \cdot a)c = b ## according to the first attachment, (Alan F. Beardon, Algebra and geometry)? λ = 1 and μ =1
He says that we should view the above equation as a line ## x + t*c = b## then substitute this x back into ## x + (x \cdot a)c = b ## but t also has x in it? As ## x + t*c = b## comes from ## x + (x \cdot a)c = b ## how can we put it back into the original equation as above?
Next, I made the substitution in the second attachment. Please explain why t is all the real numbers as solution when ## a \cdot b = 0 ## AND ## 1 + a \cdot c = 0 ##? ##\frac{0}{0}## is undefined right? is that why t can be any value?
He says that we should view the above equation as a line ## x + t*c = b## then substitute this x back into ## x + (x \cdot a)c = b ## but t also has x in it? As ## x + t*c = b## comes from ## x + (x \cdot a)c = b ## how can we put it back into the original equation as above?
Next, I made the substitution in the second attachment. Please explain why t is all the real numbers as solution when ## a \cdot b = 0 ## AND ## 1 + a \cdot c = 0 ##? ##\frac{0}{0}## is undefined right? is that why t can be any value?