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Let 𝑉 be the vector space of symmetric 2×2 matrices and 𝑊 be the subspace 𝑊=span{[4−5−50],[−2−5−51]}. a. Find a nonzero element 𝑋 in 𝑊.

 Let V" role="presentation" style="display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; background-color: rgb(245, 245, 245); position: relative;">V be the vector space of symmetric 2×2" role="presentation" style="display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; background-color: rgb(245, 245, 245); position: relative;">2×2 matrices and W" role="presentation" style="display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; background-color: rgb(245, 245, 245); position: relative;">W be the subspace

W=span{[4−5−50],[−2−5−51]}." role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">


a. Find a nonzero element X" role="presentation" style="display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; background-color: rgb(245, 245, 245); position: relative;">X in W" role="presentation" style="display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; background-color: rgb(245, 245, 245); position: relative;">W.Screen Shot 2021-12-09 at 9.16.22 PM.png

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Let 𝑉 be the vector space of symmetric 2×2 matrices and 𝑊 be the subspace 𝑊=span{[4−5−50],[−2−5−51]}. a. Find a nonzero element 𝑋 in 𝑊.
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