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X + y + w = b2x + 3y + z + 5w = 6

z + w = 4

2y + 2z + aw = 1

For what values a, b (constants) is the system:

(a) inconsistent?

(b) consistent w/ a unique sol'n?

(c) consistent w/ infinitely-many sol'ns?

Answers

Answer 1
Answer:

Answer:

(a) a=6 and b≠(11)/(4)

(b)a≠6

(c) a=6 and b=(11)/(4)

Step-by-step explanation:

writing equation in agumented matrix form

\begin{bmatrix}1 &1 & 0 &1 &b\n 2 &3 & 1 &5 &6\n 0& 0 & 1 &1 &4\n 0& 2 & 2&a &1\end{bmatrix}

now R_(2) =R_(2)-2* R_(1)

\begin{bmatrix}1 &1& 0 &1 &b\n 0 &1& 1 &3 &6-2b\n 0& 0 & 1 &1 &4\n 0& 2 & 2&a &1\end{bmatrix}

now R_(4) =R_(4)-2* R_(2)

\begin{bmatrix}1 &1& 0 &1 &b\n 0 &1& 1 &3 &6-2b\n 0& 0 & 1 &1 &4\n 0& 0 & 0 &a-6 &4b-11\end{bmatrix}

a) now for inconsistent

rank of augamented matrix ≠ rank of matrix

for that  a=6 and b≠(11)/(4)

b) for consistent w/ a unique solution

rank of augamented matrix = rank of matrix

  a≠6

c) consistent w/ infinitely-many sol'ns

  rank of augamented matrix = rank of matrix < no. of variable

for that condition

 a=6 and b=[tex]\frac{11}{4}

then rank become 3 which is less than variable which is 4.

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Answers

Answer:

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Step-by-step explanation:

16+10/5-3*2=12 true or false.

Answers

We need to follow the order of operations to get this one right. 
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Answers

Answer:

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Step-by-step explanation:

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Please answer this, I am confused (5^2)(7^2)(3^2)

Answers

Given:

The expression is:

(5^2)(7^2)(3^2)

To find:

The value of the given expression.

Solution:

We have,

(5^2)(7^2)(3^2)

On simplification, we get

(5^2)(7^2)(3^2)=(25)(49)(9)

(5^2)(7^2)(3^2)=11025

Therefore, the value of the given expression is 11025.

Hi can somebody check if this is correct please?

Answers

Answer:

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(6)and-
The terms of an expression 4x² – 3xy are:
(a) 4x and -3xy (b) 4x² and 3xy
(c) 4x² and -xy
(d) x

Answers

Answer:

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Step-by-step explanation:

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