For Exercises 27-34, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 3-4)
a.
b.
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College Algebra
- 4 2 Let C = -6 -3 (a) Find det(C). (b) Use your answer for (a) to determine whether C is invertible.arrow_forwardLet P2 be the set of all polynomials with degree ≤ 2. Does the set {6 − x², 1+x+4x², 8+2x+7x²} form a basis for P2? Prove that your answer is correct.arrow_forwardLet O be the 2 × 2 zero matrix. Let a be a real number. Prove that aO = 0.arrow_forward
- 3 11 Find B-1. Let B = 1 4arrow_forward26 5G II. 8:44 ☐ myportal.aum.edu.kw ENGLISH العربية RH Problem 2 [20 points]: Find the Reduced Row 1 4 7 Echelon Form of the matrix -1 0-1 3 04 Problem 3 [30 points]: Consider the following linear system: x+2y=1 -2x+2my=0 a) Write the linear system in the matrix form: A.X=b. b) For m=1, find the inverse of A, using the definition of the inverse. In this case, deduce the solution of the system. c) Use the definition of the inverse to find the values of m for which A is not invertible. 7 A▾ III G B I Ff▾ < ↑arrow_forwardI want a mathematical relationship with all the details, not explanations and definitionsarrow_forward
- 4 sinx cos2x+4 cos x sin2x-1=0arrow_forwardFor the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -2 -[47] A = -3 1 P = Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =arrow_forward(e) Without using a membership table, show that (A N B) U (A N B) = A. State all the rules used.arrow_forward
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