![\left[\begin{array}{cc}x-y & 2 y \\ 2 y+z & x+y\end{array}\right]=\left[\begin{array}{ll}1 & 4 \\ 9 & 5\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2ca4ce3421a2dc3e7599f50fd58c71fa_l3.png "Rendered by QuickLaTeX.com")
then write the value of 
Solution: $\text { If }\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]=\left[\begin{array}{ll} e & f \\ g & h \end{array}\right]$ Therefore $a=e, b=f, c=g, d=h$ It is given...
from the following equation : ![2\left[\begin{array}{ll} 1 & 3 \\ 0 & \mathrm{x} \end{array}\right]+\left[\begin{array}{ll} \mathrm{y} & 0 \\ 1 & 2 \end{array}\right]=\left[\begin{array}{ll} 5 & 6 \\ 1 & 8 \end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fae2ef579b0094ec795f1c62b9a4b3ba_l3.png "Rendered by QuickLaTeX.com")
Solution: It is given that $\begin{array}{l} 2\left[\begin{array}{ll} 1 & 3 \\ 0 & x \end{array}\right]+\left[\begin{array}{ll} y & 0 \\ 1 & 2...
and 
, when ![2\left[\begin{array}{cc}x & 5 \\ 7 & y-3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\ 1 & 2\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\ 15 & 14\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b289d871572f69a53ee3333c591b7fdd_l3.png "Rendered by QuickLaTeX.com")
Solution: (i) Given $2\left(\begin{array}{lc} x & 5 \\ 7 y-3 \end{array}\right)+\left(\begin{array}{c} 3-4 \\ 12 \end{array}\right)=\left(\begin{array}{cc} 7 & 6 \\ 1514 \end{array}\right)$...
and , when ![\left[\begin{array}{l}\mathrm{x}+\mathrm{y} \\ \mathrm{x}-\mathrm{y}\end{array}\right]=\left[\begin{array}{l}8 \\ 4\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4f327f4e30d328717ac87c5768d0bd84_l3.png "Rendered by QuickLaTeX.com")
![\left[\begin{array}{cc}2 x+5 & 7 \\ 0 & 3 y-7\end{array}\right]=\left[\begin{array}{cc}x-3 & 7 \\ 0 & -5\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9bc3080cd3ca5d8961ae81f2e6b07c22_l3.png "Rendered by QuickLaTeX.com")
Solution: (i) Given $\left(\begin{array}{l}\boldsymbol{x}+\boldsymbol{y} \\ \boldsymbol{x}-\boldsymbol{y}\end{array}\right)=\left(\begin{array}{l}8 \\ \mathbf{4}\end{array}\right)$. By equality of...
![A=\operatorname{diag}[2,-5,9], B=\operatorname{diag}[-3,7,14]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e915667c4dc298d0e9ed08f771e99b84_l3.png "Rendered by QuickLaTeX.com")
and ![C=\operatorname{diag}[4,-6,3]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-274f356305cd7bdb13df4255156b7ef6_l3.png "Rendered by QuickLaTeX.com")
, find: 
Solution: If $Z=\operatorname{diag}[a, b, c]$, then it can be written as $Z=\left[\begin{array}{lll} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{array}\right]$ Therefore, $A+2...
![A=\left[\begin{array}{rrr}1 & -3 & 2 \\ 2 & 0 & 2\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f1d0bfe594db55e6d03941a543e5b71b_l3.png "Rendered by QuickLaTeX.com")
and ![B=\left[\begin{array}{ccc}2 & -1 & -1 \\ 1 & 0 & -1\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bad6f5c51302ce532530299b88d44da6_l3.png "Rendered by QuickLaTeX.com")
, find a matrix 
such that 
is a zero matrix.Solution: It is given that $A+B+C$ is zero matrix i.e $A+B+C=0$ $\begin{array}{l} {\left[\begin{array}{ccc} 1 & -3 & 2 \\ 2 & 0 & 2 \end{array}\right]+\left[\begin{array}{ccc} 2...
such that 
where ![A=\left[\begin{array}{ll}3 & 1 \\ 0 & 2\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-687ea49b624f69078701c50bdfe70143_l3.png "Rendered by QuickLaTeX.com")
and ![B=\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-327689b71c17725ba5fadd5f6c04b7ea_l3.png "Rendered by QuickLaTeX.com")
Solution: It is given that $2 A-B+X=0$ $\begin{array}{l} 2\left(\left[\begin{array}{ll} 3 & 1 \\ 0 & 2 \end{array}\right]\right)-\left[\begin{array}{cc} -2 & 1 \\ 0 & 3...
![A=\left[\begin{array}{cc}-2 & 3 \\ 4 & 5 \\ 1 & -6\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c1a126b89e46fb513ab316d9ddf765f2_l3.png "Rendered by QuickLaTeX.com")
and ![B=\left[\begin{array}{cc}5 & 2 \\ -7 & 3 \\ 6 & 4\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ea823875b60d35239b7a90f86c04d7b6_l3.png "Rendered by QuickLaTeX.com")
, find a matrix such that 
Solution: It is given that $A+B-C=0$ $\begin{array}{c} {\left[\begin{array}{cc} -2 & 3 \\ 4 & 5 \\ 1 & -6 \end{array}\right]+\left[\begin{array}{cc} 5 & 2 \\ -7 & 3 \\ 6 & 4...
, if ![\left[\begin{array}{rrr}3 & 5 & -9 \\ -1 & 4 & -7\end{array}\right]+X=\left[\begin{array}{lll}6 & 2 & 3 \\ 4 & 8 & 6\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-45e666fb26d68da37727a27b2abe54f0_l3.png "Rendered by QuickLaTeX.com")
Solution: It is given that $\left[\begin{array}{ccc}3 & 5 & -9 \\ -1 & 4 & -7\end{array}\right]+x=\left[\begin{array}{lll}6 & 2 & 3 \\ 4 & 8 & 6\end{array}\right]$...
and 
, if ![2 A-B=\left[\begin{array}{rrr}6 & -6 & 0 \\ -4 & 2 & 1\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7c7e70a825c505f4ed47602a40feb33a_l3.png "Rendered by QuickLaTeX.com")
and ![2 B+A=\left[\begin{array}{ccc}3 & 2 & 5 \\ -2 & 1 & -7\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-97bab0d2cf485a48b9cadb26dc60dbb6_l3.png "Rendered by QuickLaTeX.com")
Solution: $\operatorname{Add} 2(2 A-B)$ and $(2 B+A)$ $\begin{array}{l} 2(2 A-B)+(2 B+A)=2\left(\left[\begin{array}{ccc} 6 & -6 & 0 \\ -4 & 2 & 1...
and , if ![A+B=\left[\begin{array}{ccc}1 & 0 & 2 \\ 5 & 4 & -6 \\ 7 & 3 & 8\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3a87601979fb533a239d62337a5b2064_l3.png "Rendered by QuickLaTeX.com")
and ![A-B=\left[\begin{array}{ccc}-5 & -4 & 8 \\ 11 & 2 & 0 \\ -1 & 7 & 4\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-58cb7bbac0f7ccbeaeb8025170c9380e_l3.png "Rendered by QuickLaTeX.com")
Solution: Add $(A+B)$ and $(A-B)$ We obtain $(A+B)+(A-B)=\left[\begin{array}{ccc}1 & 0 & 2 \\ 5 & 4 & -6 \\ 7 & 3 & 8\end{array}\right]+\left[\begin{array}{ccc}-5 & -4...
![5 \mathrm{~A}=\left[\begin{array}{ccc}5 & 10 & -15 \\ 2 & 3 & 4 \\ 1 & 0 & -5\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-68173ac372a0be08a045f2efa000c776_l3.png "Rendered by QuickLaTeX.com")
, find 
Solution: $5 A=\left[\begin{array}{ccc}5 & 10 & -15 \\ 2 & 3 & 4 \\ 1 & 0 & -5\end{array}\right]$ $A=\left[\begin{array}{ccc}\frac{5}{5} & \frac{10}{5} &...
![A=\left[\begin{array}{ccc}0 & 1 & -2 \\ 5 & -1 & -4\end{array}\right], B=\left[\begin{array}{ccc}1 & -3 & -1 \\ 0 & -2 & 5\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-41e2731669cc626117fcfaab4c782d70_l3.png "Rendered by QuickLaTeX.com")
and ![C=\left[\begin{array}{ccc}2 & -5 & 1 \\ -4 & 0 & 6\end{array}\right] .](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ec6db1baabfa8122c2209e13ff3fac41_l3.png "Rendered by QuickLaTeX.com")
Compute 
Solution: $\begin{array}{l} \left.5 A-3 B+4 C=5\left(\left[\begin{array}{ccc} 0 & 1 & -2 \\ 5 & -1 & -4 \end{array}\right]\right)-3\left(\begin{array}{ccc} 1 & -3 & -1 \\ 0...
![A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a7bc1c4d1eeefbbc4f83e854a1687521_l3.png "Rendered by QuickLaTeX.com")
and ![C=\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right] .](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8bd7890a3a96a4c97189a908536ad3df_l3.png "Rendered by QuickLaTeX.com")
Find: 
Solution: $\begin{array}{l} \text { i. } A-2 B+3 C \\ \text { A- } 2 B+3 C=\left[\begin{array}{ll} 2 & 4 \\ 3 & 2 \end{array}\right]-2\left(\left[\begin{array}{cc} 1 & 3 \\ -2 & 5...
and Find: 
Solution: i. $\begin{array}{l} A+2 B=\left[\begin{array}{ll} 2 & 4 \\ 3 & 2 \end{array}\right]+2\left(\left[\begin{array}{cc} 1 & 3 \\ -2 & 5 \end{array}\right]\right) \\...
![A=\left[\begin{array}{ccc}3 & 1 & 2 \\ 1 & 2 & -3\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-31a9f285753e96665b1043f971261649_l3.png "Rendered by QuickLaTeX.com")
and ![B=\left[\begin{array}{ccc}-2 & 0 & 4 \\ 5 & -3 & 2\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2db0d1cb1cd62becc5703078ca3469a4_l3.png "Rendered by QuickLaTeX.com")
, find 
Solution: $\begin{array}{l} 2 A=2\left(\left[\begin{array}{ccc} 3 & 1 & 2 \\ 1 & 2 & -3 \end{array}\right]\right) \\ =\left[\begin{array}{ccc} 6 & 2 & 4 \\ 2 & 4 & -6...
![A=\left[\begin{array}{cc}3 & 5 \\ -2 & 0 \\ 6 & -1\end{array}\right], B=\left[\begin{array}{cc}-1 & -3 \\ 4 & 2 \\ -2 & 3\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-66f7d37c6136b09956a37ec4bd7b2766_l3.png "Rendered by QuickLaTeX.com")
and ![C=\left[\begin{array}{cc}0 & 2 \\ 3 & -4 \\ 1 & 6\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e8b8119fe41187456a97ee682923debd_l3.png "Rendered by QuickLaTeX.com")
, verify that 
Solution: $\begin{array}{l} (A+B)+C=\left(\left[\begin{array}{cc} 3 & 5 \\ -2 & 0 \\ 6 & -1 \end{array}\right]+\left[\begin{array}{cc} -1 & -3 \\ 4 & 2 \\ -2 & 3...
![A=\left[\begin{array}{ccc}2 & -3 & 5 \\ -1 & 0 & 3\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c18faf5289add2dd71e42331e8e0f3fb_l3.png "Rendered by QuickLaTeX.com")
and ![B=\left[\begin{array}{ccc}3 & 2 & -2 \\ 4 & -3 & 1\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ac37f82b6c044fe5ac67eaa50137a95c_l3.png "Rendered by QuickLaTeX.com")
, verify that 
Solution: $\begin{array}{l} A+B=\left[\begin{array}{ccc} 2 & -3 & 5 \\ -1 & 0 & 3 \end{array}\right]+\left[\begin{array}{ccc} 3 & 2 & -2 \\ 4 & -3 & 1...