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Questions and Answers
What is the definition of a vector in the plane?
What is the definition of a vector in the plane?
- A matrix of real numbers
- A single real number
- A combination of real and imaginary numbers
- An ordered pair of real numbers (correct)
What does a vector in the plane have?
What does a vector in the plane have?
- Magnitude only
- Direction only
- Neither magnitude nor direction
- Magnitude and direction (correct)
In the context of vectors, when are two matrices X and Y equal?
In the context of vectors, when are two matrices X and Y equal?
- $X = Y$ if $x_1 = y_1$ and $x_2 = y_2$ (correct)
- $X = Y$ if $x_1 imes y_1 = x_2 imes y_2$
- $X = Y$ if $x_1 + y_1 = x_2 + y_2$
- $X = Y$ if $x_1 - y_1 = x_2 - y_2$
What is the definition of an n-vector?
What is the definition of an n-vector?
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What is the result of vector addition u + v for two vectors u and v?
What is the result of vector addition u + v for two vectors u and v?
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What is the norm or length of the vector 𝑢 = (1, -2, -4, 5, 3)?
What is the norm or length of the vector 𝑢 = (1, -2, -4, 5, 3)?
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In vector addition and scalar multiplication, which property states that 𝒖 + (– 𝒖) = 𝟎?
In vector addition and scalar multiplication, which property states that 𝒖 + (– 𝒖) = 𝟎?
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Which property in vector addition and scalar multiplication states that (𝑐 + 𝑑)𝒖 = 𝑐𝒖 + 𝑑𝒖?
Which property in vector addition and scalar multiplication states that (𝑐 + 𝑑)𝒖 = 𝑐𝒖 + 𝑑𝒖?
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What is the unique unit vector in the same direction as v if v = (1, -3, 4, 2)?
What is the unique unit vector in the same direction as v if v = (1, -3, 4, 2)?
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If 𝒖 = (𝒖₁, 𝒖₂, … , 𝒖ₙ) and 𝒗 = (𝒗₁, 𝒗₂, … , 𝒗ₙ), what is the result of the expression 𝒖 + 𝒗?
If 𝒖 = (𝒖₁, 𝒖₂, … , 𝒖ₙ) and 𝒗 = (𝒗₁, 𝒗₂, … , 𝒗ₙ), what is the result of the expression 𝒖 + 𝒗?
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