1. How do we denote a general m x n matrix A algebraically? What notation do we use for the (i, j)-entry of A? Give an example of a 4 x 3 matrix and circle its (2, 3)-entry. 2. What is the zero matrix? Write down the 3 x 2 zero matrix. 3. What is a submatrix? Look at the 4 x 3 matrix you wrote down for Question 1 and write down the submatrix gotten by deleting the second row and the third column. 0 1 1 3 1 2 1 -1 3 4. Let A = -2 and B = Find the matrices A+ B, A – B, and 3A. 1 2 087 1 5. Let A = [a;ij] and B = [bi.j] be m x n matrices. What is the expression for A+B? (So, if we write A + B = [ ], what expression goes in the brackets?) Can you add matrices of different sizes?

Q: 3: For the matrices, A = [1 and B = 01 -31 (a). Show that, (A+ B)" AT +B". (b), Show that, (AB)-1 =…

A: Show that  a) (A+B)T= AT +BT  b) (AB)-1= B-1A-1  For the matrix A and B .

Q: 31. If A and B are n x n matrices, then the diagonal entries of the product matrix AB are…

A: Matrix multiplication is possible only when the number of columns of first matrix are equal to the…

Q: [-3 -2 Let A= 0 -6 and b = 14 3 2 6 Determine whether b is in the column space of A.

A: If b is in column space of A then Rank (A:b)=Rank(A).

Q: Perform LU factorization for the following matrix. 1 1 1 1 L8 2 1 81 - 84

A:

Q: Which one is not an elementary row operation? O A. Interchanging two rows of a matrix. O B. Adding a…

A:

Q: For square matrices A and B, which of the matrices below are equal to AB? II. (AªB"} I. a. I only b.…

A: Solution

Q: In this case, h = k = x = a. State the elementary row operation that transforms the first matrix…

A:

Q: [1-2 Q:Evaluate A-3A+91 where A = 2 3 3 -1 and lisa unit matrix. -3 1 2 3.

A: Given: A=1-2323-1-312 To evaluate A2-3A+9I. I is a unit matrix.

Q: Find the invariant factors of the following matrix. 1 3 6. -7 3 -3 -1 4 6.

A: We can find invariant factors of matrix by calculating characteristics polynomial and then find…