Matrices Questions

Questions... (note [1 2] is top of matrix)

• 1. Add [1 2][3 4] to [4 3][2 1]
• 2. What is [4 3][2 1] - [1 2][3 4]
• 3. If a = [4 3][2 1] and b = [1 2][3 4] , what is 2a+3b?
• 4. Find AB when a=[4 9][10 3] and b=[5 8]
• 5. Find PQ when p=[3 5][0 1] and q=[4 2][-6 1]
• 6. If m=[4 2][-1 1] then what is: m^2, and m^3
• 7. Multiply [1 1 2][0 3 5] by [3 1][3 1][3 2]
• 8. Find x and y when [2 -3][1 0] x [1 x][y 2] = [-4 0][1 3]
• 9. A[-3 0][0 2] + B[4 0][0 -7/2] = [1 0][0 1]. Find the constants A and B.
• 10. M[1/root2 -1/root2][1/root2 1/root2] = [1 -1][1 1]. Find the matrix M.

1. Add [1 2][3 4] to [4 3][2 1]

2. What is [4 3][2 1] - [1 2][3 4]

3...

• 3. If a = [4 3][2 1] and b = [1 2][3 4] , what is 2a+3b?

4. Find AB when a=[4 9][10 3] and b=[5 8]

5. Find PQ when p=[3 5][0 1] and q=[4 2][-6 1]

6. If m=[4 2][-1 1] then what is: m^2 , m^3

7. Multiply [1 1 2][0 3 5] by [3 1][3 1][3 2]

8...

• 8. Find x and y when [2 -3][1 0] x [1 x][y 2] = [-4 0][1 3]

9....

• 9. A[-3 0][0 2] + B[4 0][0 -7/2] = [1 0][0 1]. Find the constants A and B.
• Here we should multiply [-3 0][0 2] by A to get: -3a+4b and [4 0][0 -7/2] by B to get: 2a+ -3/2. Also from the question we know these both must equal 1, so we can set up a simultaneous equation. -3a+4b=1 // 2a+ -3/2 = 1 -> -6a+8b=2 // 6a+ -9/2b = 3
• Solve for B to get b=7/10 , and then sub this in to an equation to work out A which is 41/40.
• So A=41/40 and B=7/10

10....

• 10. M[1/root2 -1/root2][1/root2 1/root2] = [1 -1][1 1]. Find the matrix M.
• Our first step should be to find the determinant of [1 -1][1 1] which is 2. When we square root 2 we get root2 so we know M is an enlargement with a sf of root2.
• This is matrix form is [root2 0][0 root2], so B = [root2 0][0 root2]