Matrix Methods/Linear Algebra: Please show all work and justify the answer! 1. Consider the following matrices. [-1:] 1 2 2 0 A= -10.B=3-4 and C= 3 4 5 Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (e) (4 points) AC (d) (4 points) CB
Need help!! 1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of...
Consider the following matrices: 1 2 A= 3-4 2 3 B= 3 2 1 1 0 2 C= 2 1 3 -1 1 1 1 4 5 -4 2 5 1 3 4 1 0 1 1 - 2 D= E= F 4 1 31 7 3 2 Find each of the following, if possible. If it is not possible, explain your reasoning. 1 (a) AB (9) BAT (b) BA (h) (A + B) E (C) CD + E ()...
7. Consider the following matrices 2 3-1 0 1 A=101-2 3 0 0 0-1 2 4 2 3 -1 B-101-2 0 0-1 2 3 -1 0 c=101-2 3 For each matrix, determine (a) The rank. (b) The number of free variables in the solution to the homogeneous system of equa- tions (c) A basis for the column space d) A basis for the null space for matrices A and HB e) Dimension of the column space (f) Nullity (g) Does...
Let A and E be matrices with the following sizes.A: 3 × 4 E: 4 × 3 If defined, determine the size of the matrix E − 2A. (If an answer is undefined, enter UNDEFINED.) × If not defined, explain why. E − 2A is defined. E − 2A is not defined because E and 2A have different sizes. E − 2A is not defined because E and 2A have the same size. E − 2A is not defined because the...
Exercise 1 Consider the two matrices o 3 1 0 ) Say whether the following matrix elements are defined, and if so, give their value: 13, 1M31,M22, V13, V31, /V22 (i) Write MIT and [NI in matrix array notation. (iii) Say whether the following matrices are defined (and explain why). If they are defined, compute them and write the result in matrix array notation
= Multiplication of matrices: Basic Let C= 0 and D= [-3 2 4] 4 Find CD if it is defined. Otherwise, click on "Undefined". CD - [00] 금 [000) 8 Undefined X ? Explanation Check Type here to search o
1 2 0 5 1 2 0 5 0 1. Consider the matrices A-10 0 3 | and B Ξ | 0 0 1 3 01 . Which of the following 0 0 0 1 0 0 0 0 1 statements is truc? a) None of the matrices is in reduced echelon form b) Both A and B are in reduced echelon form c) Only is in reduced echelon form d) Only B is in reduced echelon forım
(1 point) Suppose that A, B, and Care 5 x 5,5 X 6, and 6 x 9 matrices, respectively. Determine which of the following products are defined. (a) BC Answer: undefined (b) CB Answer: undefined (c) AB Answer: 5x5 (d) 42 Answer: 5x5 Note: 1) For those defined, enter the size of the resulting matrix (e.g. 3 x 4 with spaces between the numbers and x). ii)For those undefined, enter undefined.
find the eigen space of 4a and 4c Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6. Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...