Question

the span of x-axis and y-axis in V3 is.....​

Answer 1

Answer:

2526889

Step-by-step explanation:

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Answer 2

Answer:

The span of x-axis and y-axis in $V_{3}$ is $(\alpha ,0,0)$ and $(0,\beta ,0)$  respectively.

• We need to find the span of x-axis and y-axis in $V_{3}$. Therefore, clearly we need to find a vector which spans the entire x axis and y axis.
• Let us consider a vector say, (1,0,0). Let us consider the span of this vector (1,0,0). The span consists of vectors of the form $(\alpha ,0,0)$, $\alpha$ belonging to $R$, where $R$ is the set of Real Numbers. Clearly, the span of this assumed vector in $V_{3}$ is the x-axis.
• Similarly, Let us consider a vector say, (0,1,0). Let us consider the span of this vector (0,1,0). The span consists of vectors of the form $(0,\beta ,0)$, $\beta$ belonging to $R$, where $R$ is the set of Real Numbers.  Clearly, the span of this assumed vector in $V_{3}$ is the x-axis.

Hence, the span of x-axis and y-axis in $V_{3}$ is $(\alpha ,0,0)$ and $(0,\beta ,0)$  respectively.