
let a be 4x4 matrix with determinant 3. what is the determinant of 2a
Reduce the following 4x4 determinant to upper triangular form and then find the determinant. 1 0 -1 3 2 2 0 0 1 0 4 -1 0 1 -5 1
7.(6) Let A be a square matrix of size 4x4 and if det(A) = -1. Find det(3A) and the rank of A.
2. [16 marks) - T (a) Evaluate the determinant of matrix A where: ſi 3 -1 0 2 -4 A= -2 -6 2 3 37 - 38 (b) Solve the following system of equations for 23 only, by using Cramer's Rule: [Again, your answer to part(a) may be helpful!] 21 +3.02 – 23 2x2 - 4.23 - 24 -221 - 602 +213 +324 3.01 + 7.02 – 3x3 +8.04 = 1 = 0 = -2 = 0 (c) Use your...
Linear Algebra
Problem # 4 Let A be a 4x4 matrix; the row vectors are a1-(1 230); a2 (452 1):a3-(12 5 0); a4-(2 311) Find a Symmetric matrix S and a skew symmetric T such that A- S+T
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
Let A and B be square matrices and P be an invertible matrix. If A- PBP-,show that A and B have the same determinant.
Let A and B be square matrices and P be an invertible matrix. If A- PBP-,show that A and B have the same determinant.
a b с The matrix A= has a determinant of 6. d f g h 6 k (a) What is the determinant of the matrix B= 3d 29 -6f] За 2c -6b? 3h 2k -61 List the row & column 'operations' that were performed on A to produce B and state what each of these 'operations' does to the determinant. 3d (b) What is the determinant of the matrix C = 2a 39 2c 6k 3f 26 -6j -6h Explain...
Let A be a square matrix. Prove that if A2 = A, then I - 2A is the inverse of I - 2A.
4. Let B be a matrix such that -2a -3b nullspace(B)- What is the dimension of the column space of B? What is the dimension of the row space of B?
3. Explain why the determinant of a matrix that is row equivalent to the identity matrix In is nonzero.