I am needing help with knowing simplier steps to answer the following questions.

Question

I am needing help with knowing simplier steps to answer the following questions. If you could show me a simple way to do them I would gladly appreciate it.

Thanks

Test #1 Review (Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8 & 1.9) Ex1: Determine if the following systems of equations are consistent: a.) x X2 4x 15 4x1 4x2 16x. x1 4x2 x. b.) x1 x2 x x2 3x 11 Ex2: Solve the system of equations: a.) 5x1 2x2 x3 11 3x. 17 7x1 2x. b.) x1 x2 4x3 15 4x1 4x2 16x. x1 4x2 x3 c..) x1 3x2 4x. 3 3x1 9x2 10x3 5 Ex3: Determine if the followings matrices are in row echelon form, row reduced echelon form, or neither 1 0 -3 4 a.) 0 1 5 2

Explanation / Answer

Solution

Back-up Theory

A system of simultaneous equations, in matrix form, Ax = b, where A is a (m x n) matrix, x is a (n x 1) column vector and b is a (m x 1) column vector, is consistent if detA (i.e., determinant A) is not equal to zero..

Now, to work out the solution,

Part (a)

Here A = [   1   - 1      4]

[ - 4    4 - 16]

[ 1   4 1]

Det A = 1(4 + 64) – ( - 1)(- 4 + 16) + 4(- 16 - 4) = 68 + 12 – 80 = 0

=> the given system of simultaneous equations is not consistent. ANSWER

Part (b)

Here A = [1    1      1]

                [1   0   - 1]

                [0   2     3]

Det A = 1(0+ 2) – 1(3 - 0) + 1(2 - 0) = 2 - 3 + 2 = 1 0

=> the given system of simultaneous equations is consistent. ANSWER

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