Consider this matrix transformation: [[0,1],[1,0]] What is the geometric effect of this transformation? Choose 1 answer: A A reflection across the y axis B A reflection across the line y=x (c) A rotation about the origin by 90^(@) (D) A rotation about the origin by 180^(@)

Identify Matrix Transformation: Identify the matrix transformation. The given matrix is: [[0,1], [1,0]]Effect on Vector: Understand the effect of the matrix on a vector. Consider a vector (x, y). Multiplying this vector by the matrix will result in a new vector (y, x).Analyzing Transformation: Analyze the transformation. The transformation swaps the x-coordinate with the y-coordinate. This is equivalent to reflecting a point across the line y = x.Matching with Choices: Match the transformation with the given choices. The transformation is a reflection across the line y = x, which corresponds to choice B.

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Consider this matrix transformation:

[[0,1],[1,0]]
What is the geometric effect of this transformation?
Choose 1 answer:
A A reflection across the
y axis
B A reflection across the line
y=x
(c) A rotation about the origin by
90^(@)
(D) A rotation about the origin by
180^(@)

Consider this matrix transformation: $\newline$ $\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]$ $\newline$ What is the geometric effect of this transformation? $\newline$ Choose $1$ answer: $\newline$ (A) A reflection across the $y$ axis $\newline$ (B) A reflection across the line $y=x$ $\newline$ (C) A rotation about the origin by $90^{\circ}$ $\newline$ (D) A rotation about the origin by $180^{\circ}$

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Math Problems

Algebra 2

Convergent and divergent geometric series

Full solution

Q. Consider this matrix transformation:

\newline

\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]

\newline

What is the geometric effect of this transformation?

\newline

Choose

1

answer:

\newline

(A) A reflection across the

y

axis

\newline

(B) A reflection across the line

y=x

\newline

90^{\circ}

\newline

(D) A rotation about the origin by

180^{\circ}

Identify Matrix Transformation: Identify the matrix transformation. $\newline$ The given matrix is: $\newline$ \left[\begin{array}{cc}$\newline0 & 1 (\newline$1 & 0 $\newline$ \end{array}\right]\)
Effect on Vector: Understand the effect of the matrix on a vector. Consider a vector $(x, y)$ . Multiplying this vector by the matrix will result in a new vector $(y, x)$ .
Analyzing Transformation: Analyze the transformation. $\newline$ The transformation swaps the $x$ -coordinate with the $y$ -coordinate. This is equivalent to reflecting a point across the line $y = x$ .
Matching with Choices: Match the transformation with the given choices. $\newline$ The transformation is a reflection across the line $y = x$ , which corresponds to choice $B$ .