To partition a matrix is to divide it up into smaller matrices called blocks. Visually, this can be done by drawing horizontal or vertical lines to separate the matrix. Partitioning a large matrix is useful, as matrices in some applications require too much memory to even store them. If we would like to multiply two large matrices A and B to obtain AB, they can be partitioned conformally. If the partitions of A and B are comformable then the partition of the columns of A match the partition of 1 2 3 2 3 4 the rows of B. For example if A = 2 3 4 and B = 1 1 2 3 4 5 7 , then the partitions of A and B is conformal. The columns of A are divided 3 4 8 into two parts, the first consisting of 2 columns and the second of three columns. The rows of B are divided into two parts, the first part consisting of 2 rows and the second consisting of 3 rows. If a partitioning of two matrices is conformal, then we can multiply the blocks of the matrices using the row-column rule. 1. Describe in your own words what it means for the partitions of A and B to be conformable. 2. If A = and B = 1 4 5], what is the size of the matrix AB? 3. We first learned about matrix multiplication using the row-column rule. But it can be advantageous to think about matrix multiplication using the column-row rule. In this way, instead of getting a single entry of the matrix product, multiplying a column and row yields a matrix. Then those matrices are summed to get the product. Explain Theorem 10 in your own words.Let X, Y, Z, A, B, C be 4x4 matrices. Let I be the 4x4 identity matrix. If # 2 [A 2] -[8 9]. which ort , which of the following is true? O X is the inverse of A O Y is the inverse of B O Z is the inverse of B O Y is the inverse of A