describe the span of the given vectors a)geometrically and b)algebraically [0] [3] [0] , [4]

can i get some help please

what is it about

their vectors and its for linear algebra

the first one is this right: [0] [0] , algebraically it means 0 units across and 0 units up...geometically it is basically a dot. the second one: [3] [4], geometrically it is a line that is drawn from a point that can be resolved into 3 units across and 4 units up; algebraically it has a magnitude or value(length of the line) that is given by \[\sqrt{a^2 +b^2}\] which is in this case [\sqrt{3^2 +4^2}\] = 5 as a further note on geometry, imagine a straight line of length 5 units that is put at some angle on the (x,y) plane such that from its start to its endpoint is 3 units in the x direction but 4 units in the y direction

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describe teh span of the given vectors a)geomatrically and b)algebraically [1] [-1] [0] [0] [1] [-1] [-1] [0] [1]

can i get help on that Q please

this one is just like the others just that another variable (z) was introduced-not that 'z' was not present in the previous ones but the 'z' values there were 0... such as you show now are known as 3-D vectors...

check this site: http://members.tripod.com/paul_kirby/vector/VLintro.html you'll see an example of 3-D plot

a drawing is another way of describing the vector geometrically...but for a vector: [a] [b] [c], where a,b and c are values...it says that you are moving 'a' units along the x-axis, then 'b' units along the y-axis, and finally 'c' units along the z-axis...do you understand? algebraically it is the length of the resultant vector from moving from your original point to the final point: it is found by using this formula: \[\sqrt{a^{2} + b^{2} + c ^{2}}\] do you see the difference of this with the one b4?

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