Q1. Use Gaussian elimination method to solve the following system: 2x+y-32=9 -x+2y +2:= -2 3x +2y-...

 

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Q1. Use Gaussian elimination method to solve the following system: 2x+y-32=9 -x+2y +2:= -2 3x +2y- ==7 Q2. If k=3 and A = sides and show that they are equal) that: (a) (A+B) = A + BT (b) (kA)-k-¹A-¹ (c) (A-¹)² = (A²)-¹ -[27] - [22] Q3. If A= 2 -[3 ³].. (a) Verify: (A-¹)=A (b) Compute: ((54¹)-¹) Q4. Use the given information to find A (a) (34)-¹_ then: Q6. If the matrix A is Then, Q7. (optional) Let A = -[₁], then verify (compute both Q5. Assume that the given matrices are invertible, then show the following: (a) (CDEF)¹=F-E-D-IC-1 using the fact that (AB)¹ = B-¹A-¹. (b) If k0, then (A)-¹ = A-¹. and C= (b) (74¹)¹ - [32] (c) (21+4)¹-[¹] A-[88] where a and are nonzero real numbers, then find A¹, A100 and A-200 B = [8] and -[] where a, b, c and d are nonzero real numbers. (a) Find A and B-¹, (b) Show if A¹+B¹ is invertible, then A+B is invertible. Q1. Use Gaussian elimination method to solve the following system: 2x+y-32=9 -x+2y +2:= -2 3x +2y- ==7 Q2. If k=3 and A = sides and show that they are equal) that: (a) (A+B) = A + BT (b) (kA)-k-¹A-¹ (c) (A-¹)² = (A²)-¹ -[27] - [22] Q3. If A= 2 -[3 ³].. (a) Verify: (A-¹)=A (b) Compute: ((54¹)-¹) Q4. Use the given information to find A (a) (34)-¹_ then: Q6. If the matrix A is Then, Q7. (optional) Let A = -[₁], then verify (compute both Q5. Assume that the given matrices are invertible, then show the following: (a) (CDEF)¹=F-E-D-IC-1 using the fact that (AB)¹ = B-¹A-¹. (b) If k0, then (A)-¹ = A-¹. and C= (b) (74¹)¹ - [32] (c) (21+4)¹-[¹] A-[88] where a and are nonzero real numbers, then find A¹, A100 and A-200 B = [8] and -[] where a, b, c and d are nonzero real numbers. (a) Find A and B-¹, (b) Show if A¹+B¹ is invertible, then A+B is invertible.