If Ua = {(x1, x2, x3)" E R³|x1+ 2x2 + 3ax3 = a} is closed under addition, then a = 0. Prove that the above statement is true, or construct a counter-example to disprove it.
If Ua = {(x1, x2, x3)" E R³|x1+ 2x2 + 3ax3 = a} is closed under addition, then a = 0. Prove that the above statement is true, or construct a counter-example to disprove it.
If Ua = {(x1, x2, x3)" E R³|x1+ 2x2 + 3ax3 = a} is closed under addition, then a = 0. Prove that the above statement is true, or construct a counter-example to disprove it.
Transcribed Image Text:If Ua = {(x1,x2, x3)T E R³|x1 + 2x2 + 3ax3 = a} is closed under addition, then a = 0.
Prove that the above statement is true, or construct a counter-example to disprove it.
Transcribed Image Text:Set a = 0 gives U, = {(x1,x2, 13)" E R³[T1 + 2x2 = 0}. Define an operation e for the
vectors in R by the rule:
ūei = (u1, u2, u3)' + (v1, v2, v3) = (u1 + v1, u2 – V2,0)
Suppose ū, i e Uo, show that ū J e U, if and only if ū lies on the z-axis.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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