practice_midterm1

# practice_midterm1 - = ± a b b-a ² For which values of a...

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Practice Midterm 1 1a) Find the inverse of the matrix A = 1 1 1 1 2 3 1 3 6 1b) Use part a) to solve A~x = 1 0 - 1 1c) What is the kernel and the image of the linear transformation given by A? 2) Let T 1 be a linear transformation from the plane to itself with matrix A = " 1 2 1 2 1 2 - 1 2 # a) Determine what type of geometric transformation T 1 is by applying it to the standard vectors and sketching how they are transformed. b) Let T 2 be a linear transformation from the plane to itself with matrix B = ± 2 - 1 1 2 ² Interpret T 2 T 1 geometrically by applying it to the standard vectors (you may use your answer from part a). Is T 2 T 1 = T 1 T 2 ? 1

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3a) Consider a matrix of the form A
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Unformatted text preview: = ± a b b-a ² . For which values of a and b is A-1 = A . 3b) What’s the area of the parallelogram spanned by ± 3-1 ² and ± 2 4 ² ? 4a) Give an example of a 2 × 2 matrix whose image is spanned by ± 1-5 ² . 4b) Give an example of a linear transformation whose image is the plane spanned by 4 1 4 and 1 2 . 4c) Give an example of a linear transformation whose kernel is spanned by 1 1 . 5a) Suppose A is m × n . When is ker ( A ) = ~ 0? What if n > m ? 5b) Find vectors that span the kernel of A = ± 2 1 1-1 4 ² . 2...
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practice_midterm1 - = ± a b b-a ² For which values of a...

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