Matrix Operations Proficiency Test

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1. 1

   What is the result of adding the matrices A=[[1,2],[3,4]] and B=[[5,6],[7,8]]?

   A [[6,8],[10,12]] B [[6,7],[10,14]] C [[8,9],[11,16]]
2. 2

   If A=[[2,1],[0,1]] and B=[[3,0],[5,2]], what is the product AB?

   A [[8,2],[5,2]] B [[11,2],[5,2]] C [[6,0],[5,2]]
3. 3

   What is the determinant of the matrix C=[[4,3],[2,1]]?

   A 5 B 6 C -2
4. 4

   What is the transpose of matrix D=[[1,0,3],[4,5,6]]?

   A [[1,4],[0,5],[3,6]] B [[1,4],[0,5],[3,6]] C [[1,3,5],[4,6,0]]
5. 5

   If matrix E=[[1,2,3],[4,5,6]], what is the scalar multiplication 2E?

   A [[2,4,6],[8,10,12]] B [[2,2,3],[4,5,6]] C [[1,4,3],[8,5,12]]
6. 6

   Find the inverse of matrix F=[[1,2],[3,4]] if it exists.

   A [[4,-2],[-3,1]] B [[2,-1],[3,1]] C [[-2,1],[-1.5,0.5]]
7. 7

   What is the rank of the matrix G=[[1,2,3],[0,0,0],[7,8,9]]?

   A 3 B 2 C 1
8. 8

   If H is a 3x3 identity matrix, what is the result of H*[[7,8,9]]?

   A [[7,8,9]] B [[21,24,27]] C [[0,0,0]]
9. 9

   The trace of matrix I=[[5,5],[5,5]] is?

   A 5 B 10 C 0
10. 10

    Which of the following is a symmetric matrix?

    A [[4,1],[1,2]] B [[0,1],[3,2]] C [[2,3],[5,4]]