If A, B are 3 x 3 matrices such that det(AB-1) = 12 and det(A) = 4. Find 1) det(B) 2) det(AT. (3B)-1) 3) If A? + AB = { 1, find det(A + B)
Let A and B be 3x3 matrices, with det A=9 and det B = - 6. Use properties of determinants to complete parts (a) through (e) below. a. Compute det AB. det AB = (Type an integer or a fraction.) b. Compute det 5A. det 5A = (Type an integer or a fraction.) c. Compute det BT. det BT = (Type an integer or a fraction.) d. Compute det A-7. - 1 det A (Type an integer or a simplified...
4. Let A and B be 4 x 4 matrices. Suppose det A= 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-1)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. [2] and us 6. (6 points) Let vi...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det (A?)? (d) (4 points) What is det(A-?)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. and 2 6. (6 points) Let...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-')? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of A™ are linearly independent. and t = [ ] 6. (6...
[4 points Suppose A, B, and Care 5 x 5 matrices with det(A) = -2, det(B) = 10 and the columns of C are linearly dependent. Find the following or state that there is not enough information: (a) det(10B-) (b) det(AB) (c) det(CA+CB)
(1 point) If A and B are 3 x 3 matrices, det(A) = -5, det(B) = 9, then det(AB) = det(-2A) = det(AT) = det(B-1) = det(B3) =
a. Compute det \(\mathrm{AB}\).det \(\mathrm{AB}=\square\) (Type an integer or a fraction.)b. Compute det \(5 \mathrm{~A}\).det \(5 \mathrm{~A}=\square\) (Type an integer or a fraction.)c. Compute det \(\mathrm{B}^{\top}\).\(\operatorname{det} \mathrm{B}^{\top}=\square\) (Type an integer or a fraction.)d. Compute \(\operatorname{det} A^{-1}\).\(\operatorname{det} \mathrm{A}^{-1}=\square\) (Type an integer or a simplified fraction.)e. Compute det \(\mathrm{A}^{3}\).det \(\mathrm{A}^{3}=\square\) (Type an integer or a fraction.)
Linear Algebra:Question 5 [10 points] If A, B, and C are 4×4 matrices; and det(A) = 4, det(B) = −5, and det(C) = −4 then compute: Question 5 [10 points] If A, B, and C are 4x4 matrices; and det(A) = 4, det(B) = -5, and det(C)=-4 then compute: det(2CT A-18-10-1BICI) = 0
I will rate if correct 4. (10 pts) Let A,B be square matrices with the same size n × n, and let c be a constant. True or False: (a) (AB)-1- B-1A-1 (b) ABメBA in general. (c) det(AB) = det(B) * det(A) (d) (CAB)1A (e) rank(A+ B) S rank(A) + rank(B)