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+1 0changes.txt

+1 1src/sectionILT.xml

+1 1src/sectionIVLT.xml

+1 1src/sectionSLT.xml
changes.txt
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src/sectionILT.xml
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<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces. Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$. Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation. Formulate a condition on $U$ that is equivalent to $Z$ being an injective linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): $Z$ is injective if and only if $U$ is \rule{1in}{1pt}. (See <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)
+<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces. Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$. Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation. Formulate a condition on $U$ that is equivalent to $Z$ being an injective linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): $Z$ is injective if and only if $U$ is <rule width="1in" height="1pt" />. (See <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)
src/sectionIVLT.xml
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<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces. Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$. Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation. Formulate a condition on $U$ and $V$ that is equivalent to $Z$ being an invertible linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): $Z$ is invertible if and only if $U$ and $V$ are \rule{1in}{1pt}. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="MR.M60" />.)
+<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces. Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$. Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation. Formulate a condition on $U$ and $V$ that is equivalent to $Z$ being an invertible linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): $Z$ is invertible if and only if $U$ and $V$ are <rule width="1in" height="1pt" />. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="MR.M60" />.)
src/sectionSLT.xml
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<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces. Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$. Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation. Formulate a condition on $V$ that is equivalent to $Z$ being an surjective linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): $Z$ is surjective if and only if $V$ is \rule{1in}{1pt}. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)
+<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces. Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$. Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation. Formulate a condition on $V$ that is equivalent to $Z$ being an surjective linear transformation. In other words, fill in the blank to complete the following statement (and then give a proof): $Z$ is surjective if and only if $V$ is <rule width="1in" height="1pt" />. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)