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Match each linear transformation with its matrix. ? 1. [1 0 , 0 1] A. Contraction by a factor of 2 2. [0 0 , 0 1 ] B. Rotation through an angle of 90° in the counterclockwise direction ? 3. [1 0 , 0 0] C. Identity transformation ? 4. [0 -1 , 1 0 ] D. Projection onto the y-axis 5. [2 0 , 0 2] E. Dilation by a factor of 2 6 [0.5 0 , 0 0.5 ] F. Projection onto the z- axis
Match each linear transformation with its matrix. ? 1. [1 0 , 0 1] A. Contraction by a factor of 2 2. [0 0 , 0 1 ] B. Rotation through an angle of 90° in the counterclockwise direction ? 3. [1 0 , 0 0] C. Identity transformation ? 4. [0 -1 , 1 0 ] D. Projection onto the y-axis 5. [2 0 , 0 2] E. Dilation by a factor of 2 6 [0.5 0 , 0 0.5 ] F. Projection onto the z- axis
Final answer:Different matrices represent different types of linear transformations such as identity transformation, projection onto the x or y-axis, rotation through 90 degrees, dilation and contraction by a factor of 2.Explanation:In the field of linear algebra, matrices are used to representlinear transformations. Here is how you match each linear transformation with its matrix:[1 0 , 0 1] is the matrix representation of the Identity transformation, as it doesn't change the input vector.[0 0 , 0 1] signifies the Projection onto the y-axis, as it eliminates any movement along the x-axis.[1 0 , 0 0] designates the Projection onto the x-axis. This matrix nullifies any movement along the y-axis.[0 -1 , 1 0 ] describes a Rotation through an angle of 90° in the counterclockwise direction. This matrix transforms every point in the plane by rotating it 90° counterclockwise about the origin.[2 0 , 0 2] is the matrix for a Dilation by a factor of 2. This matrix enlarges every vector by a factor of 2.[0.5 0 , 0 0.5] is the matrix for a Contraction by a factor of 2. It reduces the size of every vector by a factor of 2.Learn more about Linear Transformation here:brainly.com/question/35061121#SPJ11...