Fall 2024 Midterm 1

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Fall 2024 Midterm 1

Question 1 (8 points, 1 point each)

(a) Row echelon form

(b) A square-zero matrix

(d) Scaling a matrix

(e) Comparing two matrices

(f) Solutions of a homogeneous system

(g) Matrix dimensions

(h) Skew-symmetric matrices

Question 2 (7 points total)

(a) Determinant under row operations (3 points)

(b) Determinant of an unknown factor (4 points)

Question 3 (6 points total)

(a) Eigenvalues (3 points)

(b) An eigenvector (3 points)

Question 4 (6 points total)

(a) Solve symbolically (2 points)

(b) Calculate C (4 points)

Question 5 (6 points total)

(a) Inconsistency (2 points)

(b) Solve when k=5 (4 points)

Question 6 (8 points total)

(a) Evaluate (2 points)

(b) Standard matrix (2 points)

Question 7 (5 points)

Question 8 (4 points)