Write down matrices A1, A2, A3 that correspond to the respective linear transformations of the plane: T1 = “reflection across the line y = −x” T2 = ”rotation through 900 clockwise” T3 = ”reflection across the y axis” (a) Use matrix multiplication to determine the geometric effect of a rotation through 900 clockwise followed by a reflection across the line y = −x, i.e., T2 followed by T1. (b) Use matrix multiplication to determine the combined effect of T1 followed by T2 followed by T3

Q: Determine the dot products of the following pairs of vectors. (a) (3, 5), (3, -4) (b) (2, -5, 3),…

A: Solution :-

Q: Consider A = ⟨0, 4, 2⟩, B = ⟨6, −1, 0⟩ and C = ⟨3, 0, 1⟩. draw the vectors A, B, and C in…

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Q: Find the matrix that has the effect of reflecting vectors in R2 across the x-axis, then rotating by…

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Q: Find values for the the entries in the first matrix to satisfy this equation: 0 0 5 -10 -4 7 0 0 -1…

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A: The given matrix is A=120012, v=-4-6 We have to plot the result.

Q: What does interchanging any two rows (or columns) do to the value of the determinant?

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Q: What is transformation matrix for reflecting over the y-axis? a. b. C. d. e.

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Q: Give example 2. Determinant of a 5 × 5 matrix using properties of determinants

A: The solution of the problem is given in the next steps.

Q: Write the vector (2, –3) as a linear combination of (2, –1), (–1,2) Select one: O 2/5(2, –1) +…

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Q: B = -2 {[1] ·[5]} and = {[] [4])} C 3 are bases for R². Complete the augmented matrix used to find…

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Q: Let T: R² → R² be a reflection in the x-axis. Find the image of each vector. (a) (2,7) (b) (6, -8)…

A: T: R2 - >  R2 is a inear map which is basically reflection in the x Axis. Therefore for any point…

Q: By evaluating the determinants, verify the addition rule for the 2 x 2 case: a12 a22 la21 a22 la21…

A: Determinate

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Q: Let T: R2 R be a reflection in the x-axis. Find the image of each vector. (a) (7, 6) (b) (9,-3) (c)…

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Q: Illustrate the multiplying any row (or column) by a scalar do to the determinant?

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Q: Use determinants to find y in the below equations: 7x + 5y - 3z - 16 = 0 3x - 5y + 2z+8 = 0 5x + 3y…

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Q: (-81,24,16)

A: Determinant of matrix is=-5258

Q: Explain the Determinant by Cofactors.

A: The determinant of a square matrix is a scalar value that can be used to provide important…

Q: Find the determinant of the vector A = 2i+ 5j + 6k and B = 8k

A: determinant is nothing but finding the cross product. so, determinant of two vectors A and B = A×B

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A: We use the definition of coordinate vector relative to a given basis to answer the given question.

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Q: Find the composed matrix for aligning a vector v along the unit vector j. Assume 3-D coordinate…

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Q: 1 A = -1 2 For the matrix find A° using diagonalization.

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Q: Evaluate determinant: 2 4 5 0 -1 2 3 -5 12

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