# Find A+B A=begin{bmatrix}7 & -1 2 & 9 -7 & -8 end{bmatrix} ,B=begin{bmatrix}2 & 5 -9 &0 8 & 6 end{bmatrix} a) begin{bmatrix}5 & 4 11 & 9 -15 & -2 end{bmatrix} b) begin{bmatrix}5 & -6 11 &9 -15 & -14 end{bmatrix} c) begin{bmatrix}9 & -6 -7 & 9 1 & -14 end{bmatrix} d) begin{bmatrix}9 & 4 -7 &9 1 & -2 end{bmatrix}

Question
Matrices
Find A+B
$$A=\begin{bmatrix}7 & -1 \\2 & 9 \\ -7 & -8 \end{bmatrix} ,B=\begin{bmatrix}2 & 5 \\-9 &0 \\ 8 & 6 \end{bmatrix}$$
a) $$\begin{bmatrix}5 & 4 \\11 & 9 \\ -15 & -2 \end{bmatrix}$$
b) $$\begin{bmatrix}5 & -6 \\11 &9 \\ -15 & -14 \end{bmatrix}$$
c) $$\begin{bmatrix}9 & -6 \\-7 & 9 \\ 1 & -14 \end{bmatrix}$$
d) $$\begin{bmatrix}9 & 4 \\-7 &9 \\ 1 & -2 \end{bmatrix}$$

2021-01-14
Step 1
given two matrices are
$$A=\begin{bmatrix}7 & -1 \\2 & 9 \\ -7 & -8 \end{bmatrix} \text{ and }B=\begin{bmatrix}2 & 5 \\-9 &0 \\ 8 & 6 \end{bmatrix}$$
now we have to find A +B
Step 2
using the addition property of matrices
$$A+B=\begin{bmatrix}7 & -1 \\2 & 9 \\ -7 & -8 \end{bmatrix} + \begin{bmatrix}2 & 5 \\-9 &0 \\ 8 & 6 \end{bmatrix} =\begin{bmatrix}7+2 & -1+5 \\2-9 & 9+0 \\ -7+8 & -8+6 \end{bmatrix} = \begin{bmatrix}9 & 4 \\-7 & 9 \\ 1 & -2 \end{bmatrix}$$
here option d) is correct

### Relevant Questions

Giventhe following matrices:
$$A=\begin{bmatrix}1 & 2 &9 \\ -1 & 2 &0 \\ 0&0&4 \end{bmatrix} B=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix} C=\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix} D=\begin{bmatrix}1 \\ 2 \\ -4 \end{bmatrix}$$
Identify the following:
a) A-B
b) B+C
c) C-D
d) B-C
Using givens rotation during QU factorization of the matrix A below, Make element (3,1) in A zero.
$$[A]=\begin{bmatrix}3 & 4 & 5 \\1 & 7 & 8 \\ 2 & 6 & 9\end{bmatrix}$$

$$\begin{array}{|c|c|} \hline & Housework Hours \\ \hline Gender & Sample\ Size & Mean & Standard\ Deviation \\ \hline Women & 473473 & 33.133.1 & 14.214.2 \\ \hline Men & 488488 & 18.618.6 & 15.715.7 \\ \end{array}$$

a. Based on this​ study, calculate how many more hours per​ week, on the​ average, women spend on housework than men.

b. Find the standard error for comparing the means. What factor causes the standard error to be small compared to the sample standard deviations for the two​ groups? The cause the standard error to be small compared to the sample standard deviations for the two groups.

c. Calculate the​ 95% confidence interval comparing the population means for women Interpret the result including the relevance of 0 being within the interval or not. The​ 95% confidence interval for ​$$\displaystyle{\left(\mu_{{W}}-\mu_{{M}}​\right)}$$ is: (Round to two decimal places as​ needed.) The values in the​ 95% confidence interval are less than 0, are greater than 0, include 0, which implies that the population mean for women could be the same as is less than is greater than the population mean for men.

d. State the assumptions upon which the interval in part c is based. Upon which assumptions below is the interval​ based? Select all that apply.

A.The standard deviations of the two populations are approximately equal.

B.The population distribution for each group is approximately normal.

C.The samples from the two groups are independent.

D.The samples from the two groups are random.

Use cramer's rule to determine the values of $$I_1, I_2, I_3$$ and $$I_4$$
$$\begin{bmatrix}13.7 & -4.7 & -2.2 &0 \\ -4.7 & 15.4 & 0 &-8.2 \\-2.2 & 0 & 25.4 &-22 \\ 0 & -8.2 & -22 &31.3 \end{bmatrix}\begin{bmatrix}I_1 \\ I_2 \\ I_3 \\ I_4 \end{bmatrix}=\begin{bmatrix}6 \\ -6 \\ 5 \\-9 \end{bmatrix}$$
If possible , find 2A-4B
$$A=\begin{bmatrix}-3 & 5 & -6 \\ 3 & -5 & -1 \end{bmatrix} , B=\begin{bmatrix}-6 & 8 & -3 \\ 3 & 6 & -2 \end{bmatrix}$$
a. $$\begin{bmatrix}-30 & 42 & -24 \\ 18 & 14 & -10 \end{bmatrix}$$
b. not possible
c. $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}$$
d. $$\begin{bmatrix} -9 & 13 & -9 \\ 6 & 1 & -3 \end{bmatrix}$$
c. $$\begin{bmatrix} 18 & -22 & 0 \\ -6 & -34 & 6 \end{bmatrix}$$

Use exponential regression to find a function that models the data. $$\begin{array}{|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 14 & 7.1 & 3.4 & 1.8 & 0.8 \\ \hline \end{array}$$

Refer to the following matrices.
$$A=\begin{bmatrix}2 & -3&7&-4 \\-11 & 2&6&7 \\6 & 0&2&7 \\5 & 1&5&-8 \end{bmatrix} B=\begin{bmatrix}3 & -1&2 \\0 & 1&4 \\3 & 2&1 \\-1 & 0&8 \end{bmatrix} , C=\begin{bmatrix}1& 0&3 &4&5 \end{bmatrix} , D =\begin{bmatrix}1\\ 3\\-2 \\0 \end{bmatrix}$$
Identify the row matrix. Matrix C is a row matrix.
Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B
$$A=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} ,B=\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}$$

Let M be the vector space of $$2 \times 2$$ real-valued matrices.
$$M=\begin{bmatrix}a & b \\c & d \end{bmatrix}$$
and define $$M^{\#}=\begin{bmatrix}d & b \\c & a \end{bmatrix}$$ Characterize the matrices M such that $$M^{\#}=M^{-1}$$

$$A=\begin{bmatrix}1 & -1 \\0 & 1 \end{bmatrix},B=\begin{bmatrix}2 & 3 \\1 & 5 \end{bmatrix},C=\begin{bmatrix}1 & 0 \\0 & 8 \end{bmatrix},D=\begin{bmatrix}2 & 0 &-1\\1 & 4&3\\5&4&2 \end{bmatrix} \text{ and } F=\begin{bmatrix}2 & -1 &0\\0 & 1&1\\2&0&3 \end{bmatrix}$$
(i) $$AX^T=BC^3$$
(ii) $$A^{-1}(X-T)^T=(B^{-1})^T$$
(iii) $$XF=F^{-1}-D^T$$