can you solve these truefalse questions 11 True or False TF

11. True or False TF Histograms may be constructed using either observed or relative frequencies TF A Pareto chart is usually used with categorical data. TFAll 3x3 matrices are invertible. TF Suppose that A is a 4x6 matrix and B is 6x4 matrix. Then AB is a 6x6 matrix TF Suppose that A is a 4x6 matrix and B is 6x4 matrix. Then AB is a 4x4 matrix T F Pascal\'s triangle is symmetric and has 1\'s along both sides.

Solution

I will try to give explanation wherever it is not abolutely trivial.

1. Histograms can be constructed using either observed or relative frequencies

True

2. A pareto chart is usually used with categorical data.

True

3. All 3*3 matrices are invertible.

False . Other than being a square matrix, there are other condition too for a matrix to be invertible.

4. Suppose that A is a 4*6 matrix and B is a 6*4 matrix. Then AB is a 6*6 matrix.

False , If A is a m*n matrix and B is a n*k matrix, then AB will be a m*k matrix.

5. Suppose that A is a 4*6 matrix and B is a 6*4 matrix. Then AB is a 4*4 matrix.

True. If A is a m*n matrix and B is a n*k matrix, then AB will be a m*k matrix.

6. Pascal\'s triangle is symmetric and has 1\'s along both sides.

True. It is symmetric because the number of ways of selecting r out of n object is same to selecting n-r objects out of n objects. It has one along both sides because to select a 0 or n objects out of n object we only have one way (in each case)

Please ask rest questions seperately.